Search

The modular estimates for the fractional integral operators and the k-plane transforms are obtained in this paper. These estimates are obtained by using the modular estimates of Hardy operators and the modular interpolation theorem.

In this paper we study the Riesz transforms Rw related to the Weinstein operators Δw=∑i=1dxd−2α−1(∂/∂xi)(xd2α+1(∂/∂xi)). We develop for Rw a theory that runs parallel to the one for the Euclidean Riesz Transform. It is proved that the Riesz–Weinstein transform in coordinates i=1,…,d, Rwi is actually a Calderon–Zygmund singular integral operator in the sense of the associated space of homogeneous type. Moreover, our Riesz–Weinstein transform can be written as a principal value.

We give sufficient conditions on variable exponent functions p : Rn → [1,∞) for which the higher-order Riesz transforms, associated with the Ornstein–Uhlenbeck semigroup, are bounded on Lp(·) (Rn, dγ ), where γ denotes the Gaussian measure. Fil: Dalmasso, Estefanía Dafne. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Matemática Aplicada del Litoral. Universidad Nacional del Litoral. Instituto de Matemática Aplicada del Litoral; Argentina Fil: Scotto, Roberto Aníbal. Universidad Nacional del Litoral. Facultad de Ingeniería Química; Argentina

The aim of this paper is to prove new uncertainty principles for an integral operator with a bounded kernel. To do so we prove a Nash-type inequality and a Carlson-type inequality for this transformation. From this we deduce a variation on Heisenberg’s uncertainty inequality and Faris’s local uncertainty principle. We also prove a variation on Donoho-Stark’s uncertainty principle. Our results can be applied to a wide variety of integral operators, including the Fourier transform, the Fourier-Bessel transform, the generalized Fourier transform and the-transform.

In this article, first, on the basis of Cauchy integral formulas for biregular function, we define some singular integral operators. Then we discuss the Privalov theorem of the singular integral operators.

Members of a family of averaging operators associated with systems of partial differential operators are studied as maps on a class of weighted Lebesgue spaces. Those spaces on which the operators are bounded maps are determined and the operator norms are given precisely.

We consider the following equation for the Riesz potential of order one: Uniqueness of solutions is proved in the class of solutions for which the integral is absolutely convergent for almost ever ...

This article gives some results for the weighted spherical harmonic functions. Some relations are found between the singular integral operators generated by generalized shift operator and singular pseudo-differential operators. Finally, the boundedness of the pseudo-differential operators studied are shown.

This paper represents a broadened version of the plenary lecture presented by the author at the conference Analytic Methods of Analysis and Differential Equations (AMADE-2003), September 4–9, 2003,...

This paper is devoted to the study of four integral operators, which are generalizations and modifications of integrals of Hadamard, in the space X c p of Lebesgue measurable functions f on R + = (0, ∞) such that for c ∈ R = (−∞, ∞) [Formula: See Text] Representations for the operators are given in the form of integral transforms involving the Meijer G-function in the kernels. The mapping properties such as the boundedness, representation and range are established.

In this paper we give a further development of the results of the paper [1] and apply it to convolution operators in the spaces Lp(x) . We consider the question of extendability of the Young theorem: well known for constant p and q, to the case when they may be variable. We also potential type operators with the Kernel . In section 1 we develop some estimates for Lp(x) -norms of power functions of distance truncated to exterior of a ball of radius . Section 2 deals with convolution operators in the spaces Lp(x) and Section 3 is devoted to potential type operators.

Algebras generated by two-dimensional singular integral operators in a multiconnected plain domain are considered. The corresponding symbol algebras are described, index formula for Fredholm operators is given.

(2002). A Short Proof of Lebesgue's Density Theorem. The American Mathematical Monthly: Vol. 109, No. 2, pp. 194-196.

A basic notion of pseudodifferential operators or singular integral operators is the symbol. We want to give a formula for the symbol of weakly singular integral operators. This gives a simple connection between weakly singular integral operators and a special class of pseudodifferential operators. The case of singular integral operators is included. In this way we are able to use the theory of symbols also for weakly singular integral operators.

In this note, as a consequence of the Radon-Nikodym theorem for positive operators given by Luxemburg and Schep ([6]), we obtain a Radon-Nikodym theorem for Riesz space valued measures similar to Wright's theorem ([11]).

This note presents an alternate approach to the analysis of the composition of some (classical) singular integral oprators that arise in a number of applications. It is based on the facts that certain naturally paired operators have the same range and are injective. In the course of this analysis the proofs of some classical identities are unified

(1976). A caculus of fourier integral operators on Rn and the fundamental solution for an operator of hyperbolic type. Communications in Partial Differential Equations: Vol. 1, No. 1, pp. 1-44.

In this paper, we establish that the following maximal Hilbert transform along two-sided homogeneous curves, is bounded in the mixed norm Lebesgue spaces, Lp(Lq,(S1),R2), where .