Multipliers of Laplace transform type in certain Dunkl and Laguerre settings

TL;DR

This paper studies Laplace transform multipliers in Dunkl and Laguerre settings, proving their boundedness on weighted L^p spaces using Calderón-Zygmund theory.

Contribution

It introduces new boundedness results for Laplace-type multipliers in Dunkl and Laguerre frameworks, expanding harmonic analysis tools in these contexts.

Findings

Multipliers are bounded on weighted L^p spaces for 1<p<∞

Operators are weakly bounded from L^1 to weak L^1

Uses Calderón-Zygmund theory to establish results

Abstract

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 $\mathbb{Z}_2^d$ and in the related context of Laguerre function expansions of convolution type. We use Calder\'on-Zygmund theory to prove that these multiplier operators are bounded on weighted $L^p$, $1<p<\infty$, and from $L^1$ to weak $L^1$.