Paley type inequality on Hardy space in the Dunkl setting

TL;DR

This paper extends Paley type inequalities to Hardy spaces within the Dunkl setting, analyzing key operators like the $ ext{lambda}$-Hilbert transform and Poisson integrals, thereby broadening harmonic analysis tools in this context.

Contribution

It introduces a new version of Paley type inequality for Hardy spaces in the Dunkl setting, extending previous results and analyzing related integral transforms.

Findings

Established a new Paley type inequality in Dunkl Hardy spaces.

Analyzed $ ext{lambda}$-Hilbert and Poisson integrals in this setting.

Extended classical harmonic analysis results to Dunkl operators.

Abstract

We investigate $\lambda$-Hilbert transform, $\lambda$-Possion integral and conjugate $\lambda$-Poisson integral on the atomic Hardy space in the Dunkl setting and establish a new version of Paley type inequality which extends the results in \cite{F} and \cite{ZhongKai Li 3}.