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We study minimizers of non-autonomous functionals inf/u ∫Ω φ(x, |∇u|) dx when φ has generalized Orlicz growth. We consider the case where the upper growth rate of φ is unbounded and prove the Harnack inequality for minimizers. Our technique is based on “truncating” the function φ to approximate the minimizer and Harnack estimates with uniform constants via a Bloch estimate for the approximating minimizers. [ABSTRACT FROM AUTHOR]

This paper mainly deals with regularity estimates in Orlicz spaces for the following divergence parabolic equations of p-Laplacian type with a low-order term ut -- div(|Du|p--2Du)+|u|p--2 u = div(|f|p--2 f) in ΩT := Ω×(0,T) under some proper assumptions on f(x,t) . Remarkably, the equations we have discussed here contain the low-order term |u|p--2u|. [ABSTRACT FROM AUTHOR]

In their book Randomly Normed Spaces, Haydon, Levy, and Raynaud proved that every sublattice of a Musielak-Orlicz space L ψ with random sections ψ (· , ω) in a given set D can be represented as a Musielak–Orlicz space L ψ ′ with random sections ψ ′ (· , ω) in the closure (in the product topology) of the convex hull of D. In this note we prove that if L ψ ′ is a Musielak–Orlicz space with random sections ψ ′ (· , ω) in the closure of the convex hull of a set D closed under dilations, then there exists a Musielak–Orlicz space L ψ with random sections ψ (· , ω) in D such that L ψ ′ is a sublattice of L ψ . Furthermore, L ψ can be chosen to have the same density character as L ψ ′ . [ABSTRACT FROM AUTHOR]

We establish a new characterization of the Musielak-Orlicz-Sobolev space on ℝn, which includes the classical Orlicz-Sobolev space, the weighted Sobolev space, and the variable exponent Sobolev space as special cases, in terms of sharp ball averaging functions. Even in a special case, namely, the variable exponent Sobolev space, the obtained result in this article improves the corresponding result obtained by P. Hästö and A. M. Ribeiro [Commun. Contemp. Math., 2017, 19: 1650022] via weakening the assumption f ∈ L1(ℝn) into f ∈ L1loc(ℝn), which was conjectured to be true by Hästö and Ribeiro in the aforementioned same article. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate the existence part of the discrete Orlicz Minkowski problem, which is a non-trivial extension of the discrete Lp Minkowski problem for 0 < p < 1. [ABSTRACT FROM AUTHOR]

For periodic functions of many variables, we propose a method for their approximation in the Orlicz spaces L(𝕋m). According to this method, the functions are approximated by the sums of functions of smaller number of variables each of which is piecewise-constant in one variable for fixed values of the other variables. A Jackson-type inequality is analyzed for these approximations in terms of the mixed module of continuity. [ABSTRACT FROM AUTHOR]

Abstract We study nonlinear elliptic equations of p -Laplacian type in divergence form to establish a natural Calderón–Zygmund type theory of an Orlicz space type, where the Lebesgue space is the special case with Φ (t) = t q p : Φ (| F | p) ∈ L 1 (Q 2 R) ⟹ Φ (| D u | p) ∈ L 1 (Q R). In the previous results, the estimates obtained were strictly above the natural exponents, and the function such as Φ (t) = t log (1 + t) was ruled out for the candidate of Φ. But with our approach, Φ can be selected up to the end point case of the estimates, and the functions Φ (t) = t and Φ (t) = t log (1 + t) can be additionally selected for Φ. [ABSTRACT FROM AUTHOR]

Abstract We study local quasiminimizers of the Dirichlet energy under generalized growth conditions. Special cases include standard, variable exponent and double phase growths. We show that the gradient of a local quasiminimizer has local higher integrability. [ABSTRACT FROM AUTHOR]

We study a generalized variational inequality with an irregular obstacle in the frame of Orlicz–Sobolev spaces. Over a bounded nonsmooth domain having a sufficiently flat boundary in the Reifenberg sense, a global weighted Orlicz estimate is established for the gradient of the solution to the obstacle problem assumed BMO smallness of a coefficient. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study some strongly almost convergent double sequence spaces by Riesz mean associated with four-dimensional bounded regular matrix and a Musielak–Orlicz function over n -normed spaces. We make an effort to study some topological and algebraic properties of these sequence spaces. We also study some inclusion relations between the spaces. Finally, we establish some relation between weighted lacunary statistical sequence spaces and Riesz lacunary almost statistical convergent sequence spaces over n -normed spaces. [ABSTRACT FROM AUTHOR]

Let D be the open unit disk in the complex plane C and H(D) the class of all analytic functions on D. Letφ be an analytic self-map of D and u ∊ H(D). By constructing some suitable test functions in weighted Bergman space, in this paper the boundedness and compactness of the product-type operators DnMuCφ, DnCφMu, CφDnMu, MuDnCφ, MuCφDn and CφMuDn from weighted Bergman space to Bloch-Orlicz space are characterized in terms of the symbol functions u and φ. [ABSTRACT FROM AUTHOR]

In the paper, our main aim is to generalize the dual affine quermassintegrals to the Orlicz space. Under the framework of Orlicz dual Brunn-Minkowski theory, we introduce a new affine geometric quantity by calculating the first-order variation of the dual affine quermassintegrals, and call it the Orlicz dual affine quermassintegral. The fundamental notions and conclusions of the dual affine quermassintegrals and the Minkoswki and Brunn-Minkowski inequalities for them are extended to an Orlicz setting, and the related concepts and inequalities of Orlicz dual mixed volumes are also included in our conclusions. The new Orlicz-Minkowski and Orlicz-Brunn-Minkowski inequalities in a special case yield the Orlicz dual Minkowski inequality and Orlicz dual Brunn-Minkowski inequality, which also imply the Lp-dual Minkowski inequality and Brunn-Minkowski inequality for the dual affine quermassintegrals. [ABSTRACT FROM AUTHOR]

The notion of Aleksandrov body in the classical Brunn-Minkowski theory is extended to that of Orlicz-Aleksandrov body in the Orlicz Brunn-Minkowski theory. The analogs of the Brunn-Minkowski type inequality and the first variations of volume are established via Orlicz-Aleksandrov body. We also make some considerations for the polar of Orlicz combination. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of Orlicz mixed harmonic quermassintegrals. The variational formula of harmonic quermassintegrals with respect to the Orlicz combination is proved. The Minkowski type inequality and the Brunn-Minkowski type inequality are established for Orlicz mixed harmonic quermassintegrals. [ABSTRACT FROM AUTHOR]

A stationary viscous incompressible non-Newtonian fluid flow problem is studied with a non-polynomial growth of the extra (viscous) part of the Cauchy stress tensor together with a multivalued nonmonotone frictional boundary condition described by the Clarke subdifferential. We provide an abstract result on existence of solution to a subdifferential operator inclusion and a hemivariational inequality in the reflexive Orlicz–Sobolev space setting modeling the flow phenomenon. We establish the existence result, and under additional conditions, also uniqueness of a weak solution in the Orlicz–Sobolev space to the flow problem. [ABSTRACT FROM AUTHOR]

We prove a global Orlicz estimate for the gradient of weak solutions to a class of nonlinear obstacle problems with partially regular nonlinearities in nonsmooth domains. It is assumed that the nonlinearities are merely measurable in one spatial variable and have sufficiently small BMO semi-norm in the other variables, and the boundary of underlying domain is Reifenberg flat. [ABSTRACT FROM AUTHOR]

We prove noncommutative martingale inequalities associated with convex functions. More precisely, we obtain Φ- moment analogues of the noncommutative Burkholder inequalities and the noncommutative Rosenthal inequalities for any convex Orlicz function Φ whose Matuzewska-Orlicz indices pΦ and qΦ are such that 1 < pΦ ≤ qΦ < 2 or 2 < pΦ ≤ qΦ <∞. These results generalize the noncommutative Burkholder/Rosenthal inequalities due to Junge and Xu. The key ingredient in our approach is a simultaneous version of the Burkholder inequality recently proved for the case of noncommutative Lp-spaces with 1

Modular inequalities and inequalities for the norms of Hardy-type operators on the cone Ω of positive functions and on the cone of positive decreasing functions with common weight and common Young function in a weighted Orlicz space are considered. A reduction theorem for the norm of the Hardy operator on the cone Ω is obtained. It is shown that this norm is equivalent to the norm of a modified operator on the cone of all positive functions in the space under consideration. It is proved that the modified operator is a generalized Hardy-type operator. The equivalence of modular inequalities on the cone Ω and modified modular inequalities on the cone of all positive functions in the Orlicz space is shown. A criterion for the validity of such inequalities in general Orlicz spaces is obtained and refined for weighted Lebesgue spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce some new sequence spaces of fuzzy numbers defined by lacunary ideal convergence using generalized difference matrix and Orlicz functions. We also study some algebraic and topological properties of these classes of sequences. Moreover, some illustrative examples are given in support of our results. [ABSTRACT FROM AUTHOR]

This work is concerned with the existence and multiplicity of solutions for the following class of quasilinear problems -ΔΦu + φ(|u|)u = h(εx)ƒ (u) in RN, u ∈ W1,Φ(RN), where Φ0(t) = ƒ |t| φ(s)s ds is an N-function, ΔΦ is the Φ-Laplacian operator, ε > 0 and h, ƒ are continuous functions. In the proof of our main result we have used Variational methods, Ekeland's variational principle and some properties of the Nehari manifolds. [ABSTRACT FROM AUTHOR]

In this paper, we obtain existence results of periodic solutions of hamiltonian systems in the Orlicz-Sobolev space W1LΦ([0, T]). We employ the direct method of calculus of variations and we consider a potential function F satisfying the inequality ǀ∇F(t; x)ǀ⩽b1(t)Φ (ǀxǀ) + b2(t), with b1, b2 ϵL1 and certain N-functions Φ0. [ABSTRACT FROM AUTHOR]

We study asymptotic properties of the dynamical system generated by the multidimensional Lasota equation. We give the conditions of its stability and chaos in the sense of Devaney in Orlicz spaces. We apply Matuszewska–Orlicz indices to a description of asymptotic behavior of the considered semigroup. We analyze also the conditions under which asymptotic behavior for more general form of the equation is provided. An example illustrates the criteria when the semigroups generated by the equations have not asymptotic behavior. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce the concept of strongly Nθβ (p, F, Δm, M) -- summable with respect to the Orlicz function M and examine the notions Sθβ (F, Δm) -- statistical convergence and strong Nθβ (p, F, Δm, M) -- summability for different two lacunary sequences and β e (0, 1]. Moreover, we show that a sequence is Sθβ (F, Δm) -- statistically convergent if it is strongly Nθγ (p, F, Δm, M) -- summable, where θ = {kr} and ϑ' = {sr} are two lacunary sequences and give some inclusion relations between them. INSET: 6;Δ. [ABSTRACT FROM AUTHOR]

In this paper we prove the following global weighted estimates in Orlicz spaces f ∈ L w ϕ ( Ω T ) ⇒ u , D u , D 2 u , u t ∈ L w ϕ ( Ω T ) for second-order parabolic equations of nondivergence form with small BMO coefficients { u t − a i j ( x , t ) u x i x j = f in Ω T , u ( x , t ) = 0 on ∂ p Ω T . [ABSTRACT FROM AUTHOR]

The boundedness and compactness of the weighted composition operator from F(p, q, s) spaces to nth weighted- Orlicz spaces are characterized in this paper. [ABSTRACT FROM AUTHOR]

In the present paper we introduce some applications of I-statistical convergence to form some new spaces of sequences using a sequence of Orlicz functions and matrix transformation over n-normed spaces. We also make an effort to study several properties relevant to the topological and algebraic structure of these spaces. We investigate some inclusion relations involving these spaces. [ABSTRACT FROM AUTHOR]

In this article we introduce some new sequence spaces using I-convergence and sequences of Orlicz functions, and study some basic topological and algebraic properties of these spaces. Also we investigate the relations between these spaces. [ABSTRACT FROM AUTHOR]

In a self-contained presentation, we discuss the Orlicz-Lorentz space. Also the boundedness of composition operators on Orlicz-Lorentz spaces are characterized in this paper. [ABSTRACT FROM AUTHOR]

The Orlicz–John ellipsoids, which are in the framework of the booming Orlicz Brunn–Minkowski theory, are introduced for the first time. It turns out that they are generalizations of the classical John ellipsoid and the evolved L p John ellipsoids. The analog of Ball's volume-ratio inequality is established for the new Orlicz–John ellipsoids. The connection between the isotropy of measures and the characterization of Orlicz–John ellipsoids is demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, we prove a sharp Rogers-Shephard type inequality for the Orlicz-difference body of planar convex bodies, which extend the works of Bianchini and Colesanti ( Proc. Amer. Math. Soc. 138(7) () 2575-2582). [ABSTRACT FROM AUTHOR]

We obtain structural and geometric characteristics of sets on which weak generalized localization almost everywhere is valid for multiple trigonometric Fourier series of functions in the classes $L(\log ^ + L)^{3k + 2} (\mathbb{T}^N ),1 \leqslant k \leqslant N - 2,N \geqslant 3$, in the case where the rectangular partial sums of these series have an 'index' in which exactly k components are elements of lacunary sequences. [ABSTRACT FROM AUTHOR]

The Banach-Saks index of an Orlicz-Lorentz space Λφ,w(I) for both function and sequence case, is computed with respect to its Matuszewska-Orlicz indices of φ. It is also shown that an Orlicz-Lorentz function space has weak Banach-Saks (resp., Banach-Saks) property if and only if it is separable (resp., reflexive). [ABSTRACT FROM AUTHOR]

We construct an analytic self-map Φ of the unit disk and an Orlicz function ψ for which the composition operator of symbol Φ is compact on the Hardy-Orlicz space Hψ, but not on the Bergman-Orlicz space Bψ. For that, we first prove a Carleson embedding theorem and then characterize the compactness of composition operators on Bergman-Orlicz spaces, in terms of Carleson function (of order 2). We show that this Carleson function is equivalent to the Nevanlinna counting function of order 2. [ABSTRACT FROM AUTHOR]

The paper addresses the Dirichlet problem for the doubly nonlin- ear parabolic equation with nonstandard growth conditions: ut = div (a(x,t,u)|u|α(x,t)| ∇u|p(x,t)-2 - ∇u+ f(x,t) with given variable exponents a(x,t) and p(x,t). We establish conditions on the data which guarantee the comparison principle and uniqueness of bounded weak solutions in suitable function spaces of Orlicz-Sobolev type. [ABSTRACT FROM AUTHOR]

We study the expected value of support functions of random polytopes in a certain direction, where the random polytope is given by independent random vectors uniformly distributed in an isotropic convex body. All results are obtained using probabilistic estimates in terms of Orlicz norms that were not used in this connection before. [ABSTRACT FROM AUTHOR]

The sequence space BVσ was introduced and studied by Mur-saleen[14]. In this paper we extend BVσ to 2BVσ(p; r; s) and study some properties and inclusion relations on this space. [ABSTRACT FROM AUTHOR]

Given an non necessarily linear operator T defined from an Orlicz space Lφ'(Ω, A, μ) into itself, where φ' denote the derivative of a strictly convex function φ, we give necessary and sufficient conditions on T assuring that this operator is an extended best φ-approximation operator given a suitable σ-lattice L ⊆ A. [ABSTRACT FROM AUTHOR]

Strongly absolute bases are, roughly speaking, purely nonlocally convex bases in quasi-Banach spaces. When, in addition, they are unconditional then the discrete lattice structure they induce in the space is lattice anti-Euclidean. In this brief note we characterize the complemented unconditional basic sequences in those quasi-Banach spaces with strongly absolute unconditional basis, and use this result to derive the uniqueness of unconditional basis in many classical quasi-Banach spaces. [ABSTRACT FROM AUTHOR]

The main aim of this article is to introduce a new class of sequence spaces using the concept of n-norm and to investigate these spaces for some linear topological structures as well as examine these spaces with respect to derived (n-1)-norm. We use an Orlicz function, a bounded sequence of positive real numbers and some difference operators to construct these spaces so that they become more generalized and some other spaces can be derived under special cases. These investigations will enhance the acceptability of the notion of n-norm by giving a way to construct different sequence spaces with elements in n-normed spaces. [ABSTRACT FROM AUTHOR]

In this paper we obtain a new version of the Orlicz-Pettis theorem by using statistical convergence. To obtain this result we prove a theorem of uniform convergence on matrices related to the statistical convergence. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce and study some sequence spaces which are defined by combining the concepts of a sequence of Orlicz functions, invariant mean and lacunary convergence. We also examine some topological properties of these sequence spaces and establish some elemantary connections between them. These are generalizations of those defined and studied by Savaş and Rhoades [22] and Bataineh and Azar [2] and some others before. [ABSTRACT FROM AUTHOR]

Using finite differences and entropy inequalities, the global existence of weak solutions to a multidimensional parabolic strongly coupled prey-predator model is obtained. The nonnegativity of the solutions is also shown. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we introduce some new double sequence spaces using the notions of invariant mean and Orlicz function. We also examine some properties of the resulting sequence spaces. [Copyright &y& Elsevier]

Optimal embeddings for Orlicz-Sobolev spaces of any order into Orlicz spaces and into general rearrangement invariant spaces are established. Related Poincaré inequalities both for compactly supported functions and for arbitrary functions are also derived. [ABSTRACT FROM AUTHOR]

Some necessary and sufficient conditions on rearrangement-invariant spaces A, B are stated, which provide compactness of the corresponding Sobolev embedding W A k(Ω) ↪ B(Ω) for any bounded open set Ω ⊂ ℝ n. It is shown that this property is equivalent to compactness of some integral operator of Hardy type acting from A to B. This enables the compactness problem to be connected with behaviour of the ratio of fundamental functions ϕ A( t)/ϕ B( t) at zero. We also show that any optimal Sobolev embedding is not compact and extend this result to some other Sobolev embeddings “close” to optimal one. [ABSTRACT FROM AUTHOR]

In this article, we establish sufficient conditions on the generalized Cesáro and Orlicz sequence spaces E such that the class SE of all bounded linear operators between arbitrary Banach spaces with its sequence of s-numbers belonging to E generates an operator ideal. The components of SE as a pre-quasi Banach operator ideal containing finite dimensional operators as a dense subset and its completeness are proved. Some inclusion relations between the operator ideals as well as the inclusion relations for their duals are obtained. Finally, we show that the operator ideal formed by E and approximation numbers is small under certain conditions. [ABSTRACT FROM AUTHOR]