Inequalities related to spherical harmonics associated with the Weinstein operator

Abstract

We establish a Babenko type inequality for the Weinstein transform which allows us to obtain, for , a reverse Hölder inequality for the spherical harmonics associated with the Weinstein operator. Also, we give, for , another reverse Hölder inequality obtained by using the zonal. Next, we study the weighted Pitt inequalities for the Weinstein transform. The case p = 2 is studied separately and as a consequence, we derive a logarithmic uncertainty principle for the Weinstein transform.