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MULTIPLIERS OF LAPLACE TRANSFORM TYPE IN CERTAIN DUNKL AND LAGUERRE SETTINGS

Part of: Nontrigonometric harmonic analysis Harmonic analysis in several variables

Published online by Cambridge University Press:  15 December 2011

TOMASZ Z. SZAREK
TOMASZ Z. SZAREK*
Affiliation:
Instytut Matematyczny, Polska Akademia Nauk, Śniadeckich 8, 00-956 Warszawa, Poland (email: szarektomaszz@gmail.com)
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Abstract

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We investigate Laplace type and Laplace–Stieltjes type multipliers in the d-dimensional setting of the Dunkl harmonic oscillator with the associated group of reflections isomorphic to ℤd2 and in the related context of Laguerre function expansions of convolution type. We use Calderón–Zygmund theory to prove that these multiplier operators are bounded on weighted Lp, 1<p<∞, and from L1 to weak L1.

Keywords

Ap weightCalderón–Zygmund operatorDunkl harmonic oscillatorgeneralised Hermite expansionsLaguerre expansions of convolution typemultiplier

MSC classification

Secondary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 2 , April 2012 , pp. 177 - 190
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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