Integral transforms with H-function kernels on \LLL_ν,r-Spaces

1998/05/03 by Hans-Jürgen Glaeske, Glaeske, Hans-Jürgen, Anatoly A. Kilbas +5
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.math/9805144

arxiv created 1998/05/03 · arxiv updated 2009/11/30

Abstract

Integral transforms (\boldmathHf)(x)=∫^∞₀H^m,n_{\thinspace p,q} [xt|(a_i,α_i)_1,p
(b_j,β_j)_1,q.]f(t)dt involving Fox's H-functions as kernels are studied in the spaces \Ls_ν,r of functions f such that ∫^∞₀|t^νf(t)|^r\fracdtt<∞ (1 \eqls r<∞, ν∈\Rs). Mapping properties such as the boundedness, the representation and the range of the transforms \boldmathH are given.

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