Fractional integration for Laguerre expansions
arXiv:math/9408210
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}.