Solving dual integral equations on Lebesgue spaces

Óscar Ciaurri; José Guadalupe; Mario Pérez; Juan Varona

Displaying similar documents to “Solving dual integral equations on Lebesgue spaces”

Orthogonal polynomials and middle Hankel operators on Bergman spaces

Lizhong Peng, Richard Rochberg, Zhijian Wu (1992)

Studia Mathematica

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We introduce a sequence of Hankel style operators $H^{k}$ , k = 1,2,3,..., which act on the Bergman space of the unit disk. These operators are intermediate between the classical big and small Hankel operators. We study the boundedness and Schatten-von Neumann properties of the $H^{k}$ and show, among other things, that $H^{k}$ are cut-off at 1/k. Recall that the big Hankel operator is cut-off at 1 and the small Hankel operator at 0.

Almost everywhere summability of Laguerre series. II

K. Stempak (1992)

Studia Mathematica

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Using methods from [9] we prove the almost everywhere convergence of the Cesàro means of Laguerre series associated with the system of Laguerre functions $L_{n}^{a} (x) = {(n! / Γ (n + a + 1))}^{1 / 2} e^{- x / 2} x^{a / 2} L_{n}^{a} (x)$ , n = 0,1,2,..., a ≥ 0. The novel ingredient we add to our previous technique is the $A_{p}$ weights theory. We also take the opportunity to comment and slightly improve on our results from [9].

$G$ -functions as self-reciprocal in an integral transform

Roop Narain Kesarwani (1967)

Compositio Mathematica

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A multiplier theorem for the Hankel transform.

Rafal Kapelko (1998)

Revista Matemática Complutense

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Riesz function technique is used to prove a multiplier theorem for the Hankel transform, analogous to the classical Hörmander-Mihlin multiplier theorem (Hörmander (1960)).

Almost everywhere convergence of Laguerre series

Chang-Pao Chen, Chin-Cheng Lin (1994)

Studia Mathematica

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Denseness of the spaces $Φ_{V}$ of Lizorkin type in the mixed $L^{p ̅} (ℝ^{n})$ -spaces

Stefan Samko (1995)

Studia Mathematica

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The reciprocal of the beta function and $G L (n, ℝ)$ Whittaker functions

Eric Stade (1994)

Annales de l'institut Fourier

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In this paper we derive, using the Gauss summation theorem for hypergeometric series, a simple integral expression for the reciprocal of Euler’s beta function. This expression is similar in form to several well-known integrals for the beta function itself. We then apply our new formula to the study of $G L (n, ℝ)$ Whittaker functions, which are special functions that arise in the Fourier theory for automorphic forms on the general linear group. Specifically, we deduce explicit integral...

A convolution operation for a distributional Hankel transformation

J. Betancor, B. González (1995)

Studia Mathematica

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We investigate the Hankel transformation and the Hankel convolution on new spaces of generalized functions.

On Hankel Transform of Generalized Mathieu Series

Tomovski, Živorad (2009)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: Primary 33E20, 44A10; Secondary 33C10, 33C20, 44A20 By using integral representations for several Mathieu type series, a number of integral transforms of Hankel type are derived here for general families of Mathieu type series. These results generalize the corresponding ones on the Fourier transforms of Mathieu type series, obtained recently by Elezovic et al. [4], Tomovski [19] and Tomovski and Vu Kim Tuan [20].