On fundamental harmonic analysis operators in certain Dunkl and Bessel settings

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 Calderón-Zygmund theory we prove that these objects are bounded in weighted $L^p$ spaces, $1<p<\infty$, and from $L^1$ into weak $L^1$.

26 pages. arXiv admin note: text overlap with arXiv:1011.3615 by other authors

References in corpus (3)

• Calderón-Zygmund operators in the Bessel setting
• Analysis related to all admissible type parameters in the Jacobi setting
• Riesz transform for Dunkl Hermite expansion

Cited by in corpus (2)

• On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings
• Lusin area integrals related to Jacobi expansions