Upper and lower bounds for Littlewood-Paley square functions in the Dunkl setting

TL;DR

This paper establishes bounds for Littlewood-Paley square functions in the Dunkl setting, extending harmonic analysis techniques to this generalized context.

Contribution

It provides the first comprehensive $L^p$ estimates for Littlewood-Paley square functions within the rational Dunkl framework.

Findings

Proved upper $L^p$ bounds for Dunkl Littlewood-Paley functions.

Established lower $L^p$ bounds in the Dunkl setting.

Extended classical harmonic analysis results to Dunkl operators.

Abstract

The aim of this paper is to prove upper and lower $L^p$ estimates, $1<p<\infty$, for Littlewood-Paley square functions in the rational Dunkl setting.