Fractional integration for Laguerre expansions
George Gasper, Krzysztof Stempak, Walter Trebels
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 pro. We combine this result with sufficient (p,p) multiplier criteria of Stempak and Trebels ST. The resulting sufficient (p,q) multiplier criteria are comparable with necessary ones of Gasper and Trebels laguerre.
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