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. Shlapakov1
, Megumi Saigo2
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
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).