Laeng-Morpurgo-Type Uncertainty Inequalities for the Laguerre Transform

In this work, we prove Clarkson-type and Nash-type inequalities for the Laguerre transform $\mathfrak{F}_L$ on $\mathbb{M}=0, \infty) \times \mathbb{R}$. By combining these inequalities, we show Laeng-Morpurgo-type uncertainty inequalities. We establish also a local-type uncertainty inequalities for the Laguerre transform $\mathfrak{F}_L$, and we deduce a Heisenberg-Pauli-Weyl-type inequality for this transform.