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The objective of this paper is to extend some weighted inequalities for the Weinstein transform. Especially, we are interesting in the study of the Beckner logarithmic inequality, the Shannon inequality. We give a sharp version of this inequality. Next, we establish different Sobolev type embedding theorems in our context. Finally, we deal with some uncertainty inequalities and a logarithmic uncertainty inequality for the Weistein transform.

Shannon, Sobolev and uncertainty inequalities for the Weinstein transform