On the norm of the L^p-Dunkl transform

Abstract

In this work, we establish a Babenko–Beckner-type inequality for the Dunkl transform of a radial function and Dunkl transform associated to a finite reflection group generated by the sign changes. As applications, we establish a new version of Young’s-type inequality and uncertainty relation for Renyi entropy.

Keywords:

• Fourier transform
• Dunkl operator
• Babenko inequality
• Renyi entropy

AMS Subject Classifications:

• 33C80
• 43A32
• 44A35
• 51F15

Acknowledgments

This research is supported by NPST Program of King Saud University, project number 10-MAT1293-02. I would like to thank the anonymous referees for their helpful comments and remarks.