Fractional integration for Laguerre expansions
Classical Analysis and ODEs
2008-02-03 v1
Abstract
The aim of this note is to provide a fractional integration theorem in the framework of Laguerre expansions. The method of proof consists of establishing an asymptotic estimate for the involved kernel and then applying a method of Hedberg \cite{pro}. We combine this result with sufficient multiplier criteria of Stempak and Trebels \cite{ST}. The resulting sufficient multiplier criteria are comparable with necessary ones of Gasper and Trebels \cite{laguerre}.
Cite
@article{arxiv.math/9408210,
title = {Fractional integration for Laguerre expansions},
author = {George Gasper and Krzysztof Stempak and Walter Trebels},
journal= {arXiv preprint arXiv:math/9408210},
year = {2008}
}