On weighted transplantation and multipliers for Laguerre expansions

1993/07/08 by Krzysztof Stempak, Stempak, Krzysztof, Walter Trebels +1 · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.math/9307203

openalex publication_date 1993/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the standard square--function method (based on the Poisson semigroup), multiplier conditions of Hörmander type are derived for Laguerre expansions in L^p--spaces with power weights in the A_p-range; this result can be interpreted as an ``upper end point'' multiplier criterion which is fairly good for p near 1 or near ∞ . A weighted generalization of Kanjin's \citekan transplantation theorem allows to obtain a ``lower end point'' multiplier criterion whence by interpolation nearly ``optimal'' multiplier criteria (in dependance of p, the order of the Laguerre polynomial, the weight).

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• Fractional integration for Laguerre expansions
• On a restriction problem of de Leeuw type for Laguerre multipliers

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