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In the paper the Lorentz space L p , τ (T m) , 2 π of periodic functions of many variables and spaces with mixed logarithmic smoothness is considered. Equivalent norms of a space with mixed logarithmic smoothness are found and embedding theorems are proved. [ABSTRACT FROM AUTHOR]

In this paper, we show that Fourier restriction theorem implies the maximal and variational Fourier restriction in Lorentz space frame. The key ingredient is that we work out the induction argument in Lorentz space, based on some good properties of Lorentz space. This extends Kovač's result [J. Funct. Anal., 2019, 277(10): 3355–3372] to Lorentz space frame. [ABSTRACT FROM AUTHOR]

The equivalence of the Haar system in a rearrangement invariant space on and a sequence of pairwise disjoint functions in some Lorentz space is known to imply that up to the equivalence of norms. We show that the same holds for the class of uniform disjointly homogeneous rearrangement invariant spaces and obtain a few consequences for the properties of isomorphic embeddings of such spaces. In particular, the space with is the only uniform -disjointly homogeneous rearrangement invariant space on with nontrivial Boyd indices which has two rearrangement invariant representations on the half-axis . [ABSTRACT FROM AUTHOR]

For a separable rearrangement invariant space X on [0, 1] of fundamental type we identify the set of all p ∈ [ 1 , ∞ ] such that ℓ p is finitely represented in X in such a way that the unit basis vectors of ℓ p ( c 0 if p = ∞ ) correspond to pairwise disjoint and equimeasurable functions. This can be treated as a follow up of a paper by the first-named author related to separable rearrangement invariant spaces on (0 , ∞) . [ABSTRACT FROM AUTHOR]

We view space-filling circle packings as subsets of the boundary of hyperbolic space subject to symmetry conditions based on a discrete group of isometries. This allows for the application of counting methods which admit rigorous upper and lower bounds on the Hausdorff dimension of the residual set of a generalized Apollonian circle packing. This dimension (which also coincides with a critical exponent) is strictly greater than that of the Apollonian packing. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some Liouville-type properties for the stationary incompressible MHD equations in three dimensions. Liouville-type properties are concerned with the uniqueness of trivial solutions to the stationary MHD equations. We show that the velocity field u and the magnetic field b are vanishing provided that u ∈ BMO - 1 (R 3) and b ∈ L p , ∞ (R 3) with 2 < p ≤ 6 . Moreover, we also prove that if then u and b are vanishing for the stationary 3D MHD equations with partial viscosity and partial diffusivity. [ABSTRACT FROM AUTHOR]

The paper is dedicated to the study of embeddings of the anisotropic Besov spaces B p , θ 1 , ... , θ n β 1 , ... , β n (ℝn) into Lorentz spaces. We find the sharp asymptotic behaviour of embedding constants when some of the exponents βk tend to 1 (βk < 1). In particular, these results give an extension of the estimate proved by Bourgain, Brezis, and Mironescu for isotropic Besov spaces. Also, in the limit, we obtain a link with some known embeddings of anisotropic Lipschitz spaces. One of the key results of the paper is an anisotropic type estimate of rearrangements in terms of partial moduli of continuity. [ABSTRACT FROM AUTHOR]

Let φ : [ 0 , 1) × [ 0 , ∞) → [ 0 , ∞) be a Musielak–Orlicz function and q ∈ (0 , ∞ ] . In this article, the authors characterize the martingale Musielak–Orlicz Hardy space H φ [ 0 , 1) and the martingale Musielak–Orlicz–Lorentz Hardy space H φ , q [ 0 , 1) via dyadic maximal operators. As applications, the authors prove that the maximal Fejér operator is bounded from the space H φ [ 0 , 1) to the Musielak–Orlicz space L φ [ 0 , 1) and from H φ , q [ 0 , 1) to the Musielak–Orlicz–Lorentz space L φ , q [ 0 , 1) , which further implies some convergence results of the Fejér means. [ABSTRACT FROM AUTHOR]

This article, published in Mathematical Notes, explores the representability of lr-spaces in Orlicz function spaces. The author introduces the concepts of lattice finitely representable and symmetrically finitely representable spaces and defines the sets L(X), S(X), and J(X) for a symmetric space X. The article focuses on separable Orlicz spaces and presents a theorem stating that for certain Orlicz functions, the sets S(LN), L(LN), and J(LN) coincide. The article concludes with implications and suggestions for further research. The text includes a mathematical proof of Theorem 1 by proving Proposition 1, which involves the use of Matuszewska-Orlicz indices and various inequalities. Funding support for the work is acknowledged, and references to related research are provided. [Extracted from the article]

In this paper, we investigate the 3D inhomogeneous Navier–Stokes flows with vacuum, and obtain regularity criteria and Liouville type theorems in the Lorentz space if a smooth solution (ρ , u) satisfies suitable conditions. [ABSTRACT FROM AUTHOR]

It is shown that the space is crudely finitely representable in the Lorentz space , , if and only if or . To the best of the author's knowledge, this is the first example of a "natural" rearrangement-invariant space on such that the set of all numbers for which is crudely finitely representable in is not an interval of the real line. [ABSTRACT FROM AUTHOR]

We use a fixed point theorem and an approximation scheme to obtain the existence of at least one positive solution of a p-Laplacian equation with an exponential term that may have subcritical, critical or supercritical growth. [ABSTRACT FROM AUTHOR]

We provide a constructive proof of H1 (ℝd) (the classical Hardy space) factorization in terms of fractional commutators in Lorentz spaces. As a direct application, we obtain a characterization of functions in BMO space. Furthermore, we also obtain a Lorentz compactness characterization of fractional commutators. [ABSTRACT FROM AUTHOR]

The paper considers spaces of periodic functions of several variables, namely, the Lorentz space L q , τ (T m) , the class of functions with bounded mixed fractional derivative W q , τ r ¯ , 1 < q , τ < ∞ , and studies the order of the best M-term approximation of a function f ∈ L p , τ (T m) by trigonometric polynomials. The article consists of the introduction, the main part, and the conclusion. In the introduction, we introduce basic concepts, definitions, and necessary statements for the proof of the main results. You can also find information about previous results on the topic. In the main part, we establish exact-order estimates for the best M-term approximations of functions of the class W q , τ 1 r ¯ in the norm of the space L p , τ 2 (T m) for various relations between the parameters p , q , τ 1 , τ 2 . [ABSTRACT FROM AUTHOR]

For a separable rearrangement invariant space X on (0 , ∞) of fundamental type we identify the set of all p ∈ [ 1 , ∞ ] such that ℓ p is finitely represented in X in such a way that the unit basis vectors of ℓ p ( c 0 if p = ∞ ) correspond to pairwise disjoint and equimeasurable functions. This characterization hinges upon a description of the set of approximate eigenvalues of the doubling operator x (t) ↦ x (t / 2) in X. We prove that this set is surprisingly simple: depending on the values of some dilation indices of such a space, it is either an interval or a union of two intervals. We apply these results to the Lorentz and Orlicz spaces. [ABSTRACT FROM AUTHOR]

The logarithm space Lp log L can be defined by two equivalent, but very differently looking norms. In this note we give estimates for the best constants for the ratio of these norms. [ABSTRACT FROM AUTHOR]

Let (Ω , F , P) be a probability space, φ : Ω × [ 0 , ∞) → [ 0 , ∞) a Musielak–Orlicz function, and q ∈ (0 , ∞ ] . In this article, the authors introduce five martingale Musielak–Orlicz–Lorentz Hardy spaces and prove that these new spaces have some important features such as atomic characterizations, the boundedness of σ -sublinear operators, and martingale inequalities. This new scale of martingale Hardy spaces requires the introduction of the Musielak–Orlicz–Lorentz space L φ , q (Ω) . In particular, the authors show that this Lorentz type space has some fundamental properties including the completeness, the convergence, real interpolations, and the Fefferman–Stein vector-valued inequality for the Doob maximal operator. As applications, the authors prove that the maximal Fejér operator is bounded from the martingale Musielak–Orlicz–Lorentz Hardy space H φ , q [ 0 , 1) to L φ , q [ 0 , 1) , which further implies some convergence results of the Fejér means. Moreover, all the above results are new even for Musielak–Orlicz functions with particular structure such as weight, weight Orlicz, and double-phase growth. The main approach used in this article can be viewed as a combination of the stopping time argument in probability theory and the real-variable technique of function spaces in harmonic analysis. [ABSTRACT FROM AUTHOR]

We study mapping properties of the centered Hardy–Littlewood maximal operator M acting on Lorentz spaces L p , q (X) in the context of certain non-doubling metric measure spaces X . The special class of spaces for which these properties are very peculiar is introduced and many examples are given. In particular, for each p 0 , q 0 , r 0 ∈ (1 , ∞) with r 0 ≥ q 0 we construct a space X for which the associated operator M is bounded from L p 0 , q 0 (X) to L p 0 , r (X) if and only if r ≥ r 0 . [ABSTRACT FROM AUTHOR]

A complete description of multipliers of Fourier–Haar series in Lorentz spaces is given. Necessary and sufficient conditions for sequences of complex numbers to belong to the class of multipliers of Fourier–Haar series are obtained. [ABSTRACT FROM AUTHOR]

Let X (R) be a separable Banach function space such that the Hardy-Littlewood maximal operator is bounded on X (R) and on its associate space X ′ (R) . The algebra C X (R ˙) of continuous Fourier multipliers on X (R) is defined as the closure of the set of continuous functions of bounded variation on R ˙ = R ∪ { ∞ } with respect to the multiplier norm. It was proved by C. Fernandes, Yu. Karlovich and the first author [11] that if the space X (R) is reflexive, then the ideal of compact operators is contained in the Banach algebra A X (R) generated by all multiplication operators aI by continuous functions a ∈ C (R ˙) and by all Fourier convolution operators W 0 (b) with symbols b ∈ C X (R ˙) . We show that there are separable and non-reflexive Banach function spaces X (R) such that the algebra A X (R) does not contain all rank one operators. In particular, this happens in the case of the Lorentz spaces L p , 1 (R) with 1 < p < ∞ . [ABSTRACT FROM AUTHOR]

In this paper we give a simple proof of an estimate for Bessel potentials acting on Lorentz spaces in the supercritical exponent: let 1 < p = d α - 1 and 1 ≤ q ≤ + ∞ . If f ∈ L p , q (R d) , then there exists a constant C = C (α , d , p , q) such that | g α ∗ f (x) - g α ∗ f (z) | ≤ C | x - z | | ln (| x - z |) | + 1 1 q ′ ‖ f ‖ L p , q . [ABSTRACT FROM AUTHOR]

We refine some earlier results by Flores, Hernández, Semenov, and Tradacete on compactness of the square of strictly singular endomorphisms and identifying general Banach lattices with the Kato property in the setting of rearrangement invariant spaces on [0, 1]. A Banach space X is said to have the Kato property if every strictly singular operator acting in X is compact. We show that each strictly singular operator bounded in a disjointly homogeneous rearrangement invariant space with the non-trivial Boyd indices has compact square, and that the Kato property is shared by a 2-disjointly homogeneous rearrangement invariant space X whenever X ⊃ G , where G is the closure of L ∞ in the Orlicz space, generated by the function e u 2 - 1 . Moreover, a partial converse to the latter result is given under the assumption that X ⊂ L log 1 / 2 L . As an application we find rather sharp conditions, under which a Lorentz space Λ (2 , ψ) possesses the Kato property. In particular, Λ (2 , log - α (e / u)) , with 0 < α ≤ 1 , is a 2-DH and 2-convex rearrangement invariant space, which does not have the Kato property. This gives a negative answer to the question posed by Hernández, Semenov, and Tradacete. [ABSTRACT FROM AUTHOR]

Let X be an arbitrary separable symmetric function space on [0, 1]. By using a combination of the frame approach and the notion of the multiplicator space M (X) of X with respect to the tensor product, we investigate the problem when the sequence of dyadic dilations and translations of a function f ∈ X is a representing system in the space X. The main result reads that this holds whenever ∫ 0 1 f (t) d t ≠ 0 and f ∈ M (X). Moreover, the condition f ∈ M (X) turns out to be sharp in a certain sense. In particular, we prove that a decreasing nonnegative function f, f ≠ 0 , from a Lorentz space Λ φ generates an absolutely representing system of dyadic dilations and translations in Λ φ if and only if f ∈ M (Λ φ). [ABSTRACT FROM AUTHOR]

Conditions under which the system of dilations and translations of a function f in a symmetric space X is a representing system in X are found. Previously a similar result was known only for the spaces Lp, 1 ⩽ p < ∞. In particular, each function f with ∫ 0 1 f (t) d t ≠ 0 in a Lorentz space Λϕ generates an absolutely representing system of dilations and translations in this space if and only if the function ϕ(t) is submultiplicative. The key role in the proof is played by the notion of the multiplier space with respect to tensor product. [ABSTRACT FROM AUTHOR]

In this paper geometrical aspects of perfect fluid spacetime with torse-forming vector field ξ are described and Ricci soliton in perfect fluid spacetime with torse-forming vector field ξ are determined. Conditions for the Ricci soliton to be expanding, steady or shrinking are also given. [ABSTRACT FROM AUTHOR]

We show a factorization through Lorentz spaces for Banach-space-valued operators defined in Banach function spaces. Although our results are inspired in the classical factorization theorem for operators from Ls-spaces through Lorentz spaces Lq,1 due to Pisier, our arguments are different and essentially connected with Maurey's theorem for operators that factor through Lp-spaces. As a consequence, we obtain a new characterization of Lorentz Lq,1-spaces in terms of lattice geometric properties, in the line of the (isomorphic) description of Lp-spaces as the unique ones that are p-convex and p-concave. [ABSTRACT FROM AUTHOR]

We study the question of the continuity of functions for which the generalized gradient belongs to the Lorentz spaces. [ABSTRACT FROM AUTHOR]

The method of using rearrangements to give sufficient conditions for Fourier inequalities between weighted Lebesgue spaces is revisited, a comparison between two known sufficient conditions is completed, and the method is extended to provide sufficient conditions for a new range of indices. When 1, simple conditions on weights ensure that the Fourier transform will map a weighted Lp space into a weighted Lq space. These are established in Theorems 1 and 4 of Benedetto and Heinig (J Fourier Anal Appl 9(1):1-37, 2003). The proofs apply when 2 and 1 but not in the remaining case, 1. Here, counterexamples are given to show that these simple conditions are no longer sufficient when 1. Also, various additional conditions are presented, any of which will restore sufficiency in that case. [ABSTRACT FROM AUTHOR]

We study Kadec-Klee properties with respect to global (local) convergence in measure in quasi-Banach function spaces. First, we prove some general results which can be of independent interest. Next, we investigate these properties in symmetrizations E∗. Finally, we apply general results to study these properties in Marcinkiewicz and Lorentz spaces. [ABSTRACT FROM AUTHOR]

We consider the anisotropic Lorentz space of periodic functions. Sufficient conditions are proved for a function to belong to the anisotropic Lorentz space. Estimates for the order of approximation by trigonometric polynomials of the Nikol’skii-Besov class in the anisotropic Lorentz space are established. [ABSTRACT FROM AUTHOR]

We obtain a necessary and sufficient condition for the sums f or g of cosine or sine series with general monotone coefficients to belong to the Lorentz space Λ( q, ϕ) in terms of these coefficients { a }. Similar results are also obtained for weighted L spaces. As a corollary, the equivalence of norms of f or g in Lorentz space and corresponding weighted L space with norms of { a } in appropriate weighted l space is established. The results of this paper generalize earlier results of Booton, Dyachenko, Simonov and Tikhonov. [ABSTRACT FROM AUTHOR]

We prove the $$C^1$$ -regularity for local minima to the functionals with p( x)-growth such that $$w\mapsto \int _\Omega \left[ f(x,w,Dw)+gw\right] \, \mathrm{d}x$$ , where f satisfies a certain p( x)-growth condition. We assume that g belongs to the Lorentz space $$L^{n,1}$$ , and that $$p(\cdot )$$ and $$f(\cdot ,z,\xi )$$ satisfy Dini type continuity conditions. Our assumptions are sharp with respect to the type of regularity results obtained. [ABSTRACT FROM AUTHOR]

Series in multiplicative systems χ with generalized monotone coefficients are studied. Necessary and sufficient Hardy-Littlewood type conditions for the sums of such series to belong to the Lorentz space are proved. As corollaries, we establish estimates of best approximation in the system χ and Konyushkov-type theorems on the equivalence of O- and ≍-relations for the weighted sums of the Fourier coefficients in the system χ and for the best approximations. [ABSTRACT FROM AUTHOR]

For rough Hausdorff type operator defined on p-adic linear space Q and its commutator with symbol from Lipschitz space, we give sufficient conditions of their boundedness from one Lorentz space into another. [ABSTRACT FROM AUTHOR]

Let f and g be functions from different Lorentz spaces L [0, 1), h be theirmultiplicative convolution and xxxx be Fourier coefficients of h with respect to a multiplicative system with bounded generating sequence. We estimate the remainder of the series of xxxx with multiplicators of type k in terms of the best approximations of f and g in the corresponding Lorentz spaces. We establish sharpness of this result and of its corollaries for the Lebesgue spaces. [ABSTRACT FROM AUTHOR]

The Lorentz space with anisotropic norm of periodic functions of several variables is considered. Estimates for the Kolmogorov widths of the Nikol'skii-Besov-Amanov classes in the Lorentz space with anisotropic norm are found. [ABSTRACT FROM AUTHOR]

Given a set-function $$\psi $$ defined on bounded subsets of a Banach space with certain properties, necessary and sufficient criteria for $$\psi (A(U))=0$$ are given, when A is positively homogeneous of some order and U is bounded. The results are applied to give necessary and sufficient criteria for the compactness and weak compactness of a Fréchet derivative (in some point or at $$\infty $$ ) and when an operator is improving. [ABSTRACT FROM AUTHOR]

The Fourier coefficient map is considered as an operator from a weighted Lorentz space on the circle to a weighted Lorentz sequence space. For a large range of Lorentz indices, necessary and sufficient conditions on the weights are given for the map to be bounded. In addition, new direct analogues are given for known weighted Lorentz space inequalities for the Fourier transform. Applications are given that involve Fourier coefficients of functions in LogL and more general Lorentz-Zygmund spaces. [ABSTRACT FROM AUTHOR]

In this note we consider Wente's type inequality on the Lorentz-Sobolev space. If $$\nabla f \in {L^{{p_1},{q_1}}}{\left( R \right)^n},\;G \in {L^{{p_2},{q_2}}}{\left( R \right)^n}$$ and div G ≡ 0 in the sense of distribution where it is known that G · ∇ f belongs to the Hardy space H and furthermore . Reader can see [9] Section 4. Here we give a new proof of this result. Our proof depends on an estimate of a maximal operator on the Lorentz space which is of some independent interest. Finally, we use this inequality to get a generalisation of Bethuel's inequality. [ABSTRACT FROM AUTHOR]

Let p ∈ (0, 1], q ∈ (0,∞] and A be a general expansive matrix on ℝ. We introduce the anisotropic Hardy-Lorentz space H (ℝ) associated with A via the non-tangential grand maximal function and then establish its various real-variable characterizations in terms of the atomic and the molecular decompositions, the radial and the non-tangential maximal functions, and the finite atomic decompositions. All these characterizations except the ∞-atomic characterization are new even for the classical isotropic Hardy-Lorentz spaces on ℝ. As applications, we first prove that H (ℝ) is an intermediate space between $$H_A^{{p_1},{q_1}}\left( {{\mathbb{R}^n}} \right)$$ and $$H_A^{{p_2},{q_2}}\left( {{\mathbb{R}^n}} \right)$$ with 0 < p < p < p < ∞ and q , q, q ∈ (0,∞], and also between $$H_A^{p,{q_1}}\left( {{\mathbb{R}^n}} \right)$$ and $$H_A^{p,{q_2}}\left( {{\mathbb{R}^n}} \right)$$ with p ∈ (0,∞) and 0 < q < q < q ⩽ ∞ in the real method of interpolation. We then establish a criterion on the boundedness of sublinear operators from H (ℝ) into a quasi-Banach space; moreover, we obtain the boundedness of δ-type Calderón-Zygmund operators from H (ℝ) to the weak Lebesgue space L (ℝ) (or to H (ℝ) in the critical case, from H (ℝ) to L (ℝ) (or to H (ℝ)) with $$\delta \in \left( {0,\frac{{In{\lambda _ - }}}{{Inb}}} \right]\;,\;p \in \left( {\frac{1}{{1 + \delta }},\;1} \right]\;and\;q \in \left( {0,\;\infty } \right]$$ and q ∈ (0,∞], as well as the boundedness of some Calderón-Zygmund operators from H (ℝ) to L (ℝ), where $$b\;: \in \left| {\det \;A} \right|$$ , $${\lambda _ - }\;: = \;\min \left\{ {\left| \lambda \right|\;:\lambda \; \in \;\sigma \left( A \right)} \right\}$$ and σ( A) denotes the set of all eigenvalues of A. [ABSTRACT FROM AUTHOR]

We prove a theorem of Riesz characterizing the convergence in spaces of functions N generated by concave functions ɸ. [ABSTRACT FROM AUTHOR]

It is shown both locally and globally that $${L_t^{\infty}(L_x^{3,q})}$$ solutions to the three-dimensional Navier-Stokes equations are regular provided $${q\neq\infty}$$ . Here $${L_x^{3,q}}$$ , $${0 < q \leq\infty}$$ , is an increasing scale of Lorentz spaces containing $${L^3_x}$$ . Thus the result provides an improvement of a result by Escauriaza et al. (Uspekhi Mat Nauk 58:3-44, ; translation in Russ Math Surv 58, 211-250, ), which treated the case q = 3. A new local energy bound and a new $${\epsilon}$$ -regularity criterion are combined with the backward uniqueness theory of parabolic equations to obtain the result. A weak-strong uniqueness of Leray-Hopf weak solutions in $${L_t^{\infty}(L_x^{3,q})}$$ , $${q\neq\infty}$$ , is also obtained as a consequence. .. [ABSTRACT FROM AUTHOR]

We give a sharp condition on the lower local Lipschitz constant of a mapping from a metric space supporting a Poincaré inequality to a Banach space with the Radon-Nikodym property that guarantees differentiability at almost every point. We apply these results to obtain a non-embedding theorem for a corresponding class of mappings. [ABSTRACT FROM AUTHOR]

We establish the embeddings of the Sobolev space W and the space B (in the case of the limit exponent) in the spaces of locally summable functions of zero smoothness. This refines the embeddings of the Sobolev space in the Lorentz space and in the Lorentz-Zygmund space. The relationship between the Lorentz spaces and the corresponding spaces of functions of zero smoothness is established. Similar embeddings of the spaces of potentials are determined. [ABSTRACT FROM AUTHOR]

Dupin cyclides form a 9-dimensional set of surfaces which are, from the viewpoint of differential geometry, the simplest after planes and spheres. We prove here that, given three oriented contact conditions, there is in general no Dupin cyclide satisfying them, but if the contact conditions belong to a codimension one subset, then there is a one-parameter family of solutions. [ABSTRACT FROM AUTHOR]

We use an estimate of the $$k$$ -modulus of smoothness of a function $$f$$ such that the norm of its distributional gradient $$|\nabla ^kf|$$ belongs locally to the Lorentz space $$L^{n/k, 1}({\mathbb {R}}^n),\,k \in {\mathbb {N}},\,k\le n$$ , and we prove its reverse form to establish necessary and sufficient conditions for continuous embeddings of Sobolev-type spaces. These spaces are modelled upon rearrangement-invariant Banach function spaces $$X({\mathbb {R}}^n)$$ . Target spaces of our embeddings are generalized Hölder spaces defined by means of the $$k$$ -modulus of smoothness $$(k\in {\mathbb {N}})$$ . General results are illustrated with examples. [ABSTRACT FROM AUTHOR]

In this paper, we prove the O'Neil inequality for the k-linear convolution operator in the Lorentz spaces. As an application, we obtain the necessary and sufficient conditions on the parameters for the boundedness of the k-sublinear fractional maximal operator MΩ,α(f) and the k-linear fractional integral operator IΩ,α(f) with rough kernels from the spaces Lp1r1 × Lp2r2 ו • •× Lpkrk to Lqs, where n/(n + α) ≤ p < q < ∞, 0 < r ≤ s < ∞, p is the harmonic mean of p1, p2, . . . , pk > 1 and r is the harmonic mean of r1, r2, . . . , rk > 0. [ABSTRACT FROM AUTHOR]

In the recent study of infinite root systems, fractal patterns of ball packings were observed while visualizing roots in affine space. In this paper, we show that the observed fractals are exactly the ball packings described by Boyd and Maxwell. This correspondence is a corollary of a more fundamental result: given a geometric representation of a Coxeter group in a Lorentz space, the set of limit directions of weights equals the set of limit roots. Additionally, we use Coxeter complexes to describe tangency graphs of the corresponding Boyd-Maxwell ball packings. Finally, we enumerate the Coxeter systems that generate Boyd-Maxwell ball packings. [ABSTRACT FROM AUTHOR]

In this paper we study the norm of the Rademacher sums for some class of rearrangement invariant spaces and find its asymptotic behavior with the growth of the number of summands. [ABSTRACT FROM AUTHOR]