International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 713-722
doi:10.1155/S0161171298000994

On inversion of H-transform in 𝔏v,r-space

Sergei A. Shlapakov,1 Megumi Saigo,2 and Anatoly A. Kilbas3

1Department of Mathematics, Vitebsk Pedagogical University, Vitebsk 210036, Belarus
2Department of Applied Mathematics, Fukuoka University, Fukuoka 814-0180, Japan
3Department of Mathematics and Mechanics, Belarusian State University, Minsk 220050, Belarus

Received 1 December 1995; Revised 25 September 1997

Copyright © 1998 Sergei A. Shlapakov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The paper is devoted to study the inversion of the integral transform (Hf)(x)=∫0∞Hp,qm,n[xt|(ai,αi)1,p(bj,βj)1,p|]  f(t)dt involving the H-function as the kernel in the space 𝔏v,r of functions f such that ∫0∞|tυf(t)|rdtt<∞  (1<r<∞,ν∈ℝ).