Laeng-Morpurgo-type uncertainty inequalities for the Weinstein transform

Abstract

In this work, by combining Carlson-type and Nash-type inequalities for the Weinstein transform $\mathscr{F}_W$ on $\mathbb{K}=\mathbb{R}^{d-1}\times[0,\infty)$, we show Laeng-Morpurgo-type uncertainty inequalities. We establish also local-type uncertainty inequalities for the Weinstein transform $\mathscr{F}_W$, and we deduce a Heisenberg-Pauli-Weyl-type inequality for this transform.