On Lusin's area integrals and g-functions in certain Dunkl and Laguerre settings

TL;DR

This paper studies g-functions and Lusin's area integrals in Dunkl and Laguerre frameworks, proving their boundedness on weighted L^p spaces and weak L^1, advancing harmonic analysis in these settings.

Contribution

It establishes boundedness properties of square functions in Dunkl and Laguerre contexts, a novel extension in harmonic analysis.

Findings

Boundedness of g-functions on weighted L^p spaces

Weak L^1 boundedness of Lusin's area integrals

Extension of harmonic analysis tools to Dunkl and Laguerre settings

Abstract

We investigate $g$-functions and Lusin's area type integrals related to certain multi-dimensional Dunkl and Laguerre settings. We prove that the considered square functions are bounded on weighted $L^p$, $1<p<\infty$, and from $L^1$ into weak $L^1$.