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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 weightedPitt 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.

Inequalities related to spherical harmonics associated with the Weinstein operator