Fractional integration for Laguerre expansions

Details Fractional integration for Laguerre expansions Fractional integration for Laguerre expansions

1994-08-31

arxiv.org/abs/math/9408210v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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 $(p,p)$ multiplier criteria of Stempak and Trebels \cite{ST}. The resulting sufficient $(p,q)$ multiplier criteria are comparable with necessary ones of Gasper and Trebels \cite{laguerre}.

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