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

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.

arXiv comment9 pages

References in corpus (1)

• Uncertainty principles for integral operators

Cited by in corpus (1)

• Hardy-type inequalities for fractional powers of the Dunkl--Hermite operator