English

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 (p,p)(p,p) multiplier criteria of Stempak and Trebels \cite{ST}. The resulting sufficient (p,q)(p,q) 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}
}