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arXiv · 1304.2904

On fundamental harmonic analysis operators in certain Dunkl and Bessel settings

Alejandro J. Castro·Tomasz Z. Szarek
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Abstract

We consider several harmonic analysis operators in the multi-dimensional context of the Dunkl Laplacian with the underlying group of reflections isomorphic to $\mathbb{Z}_2^n$ (also negative values of the multiplicity function are admitted). Our investigations include maximal operators, $g$-functions, Lusin area integrals, Riesz transforms and multipliers of Laplace and Laplace-Stieltjes transform type. Using the general Calder\'on-Zygmund theory we prove that these objects are bounded in weighted $L^p$ spaces, $1<p<\infty$, and from $L^1$ into weak $L^{1}$.

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Alejandro J. Castro, Tomasz Z. Szarek. 2013-04-10. On fundamental harmonic analysis operators in certain Dunkl and Bessel settings. https://doi.org/10.1016/j.jmaa.2013.11.020

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