Sharp Pitt inequality and logarithmic uncertainty principle for Dunkl transform in $L^{2}$

TL;DR

This paper establishes a sharp version of Pitt's inequality and a logarithmic uncertainty principle for the Dunkl transform in L^2 space, advancing the understanding of harmonic analysis in this context.

Contribution

It introduces the first sharp Pitt's inequality for the Dunkl transform in L^2 and derives a related logarithmic uncertainty principle, extending classical results to Dunkl analysis.

Findings

Proved sharp Pitt's inequality for Dunkl transform in L^2

Derived the logarithmic uncertainty principle for Dunkl transform

Extended harmonic analysis inequalities to Dunkl setting

Abstract

We prove sharp Pitt's inequality for the Dunkl transform in $L^{2}(\mathbb{R}^{d})$ with the corresponding weights. As an application, we obtain the logarithmic uncertainty principle for the Dunkl transform.