Hardy-Titchmarsh And Hankel Type Transforms In [image omitted]-Spaces
Title:
Hardy-Titchmarsh And Hankel Type Transforms In [image omitted]-Spaces
Author:
Kilbas, A. A. Borovco, A. N.
Appeared in:
Integral transforms and special functions
Paging:
Volume 10 (2000) nr. 3-4 pages 239-266
Year:
2000-12
Contents:
The paper is devoted to study the integral transform [image omitted] containing the Gauss hypergeometric function [image omitted] in the kernel with complex [image omitted] b, c on the space [image omitted] of Lebesgue measurable functions f on R+ such that [image omitted] ; [image omitted] When a=ν+σ+1/2b=η+σ+1/2 and c=2η+σ+1, the transform Ja,b,cf coincides (with the exactness to the multiplier) with the transform studied by Titchmarsh, while for a = 1b = σ + 1 and c = η+σ+1, Ja,b,cf is a modification of the transform studied by Hardy. The Hankel and extended Hankel transforms are deduced from the latter transform when σ = 0 and σ = 1 ε N0 = {0,1,2,...}, respectively. Mapping properties such as the boundedness, the representation, the range and the inversion of the transform Ja,b,cf are proved. The corresponding results for the Titchmarsh, modified Hardy, extended Hankel and Hankel transforms are given.
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