On the norm of theLp-Dunkl transform

AbstractIn 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 transformDunkl operatorBabenko inequalityRenyi entropyAMS Subject Classifications: 33C8043A3244A3551F15 AcknowledgmentsThis 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.