Fethi SOLTANI.Laeng-Morpurgo-Type Uncertainty Inequalities for the Laguerre Transform[J].数学研究及应用,2022,42(1):8~14
Laeng-Morpurgo-Type Uncertainty Inequalities for the Laguerre Transform
Laeng-Morpurgo-Type Uncertainty Inequalities for the Laguerre Transform

DOI：10.3770/j.issn:2095-2651.2022.01.002

 作者 单位 Fethi SOLTANI Facult\'e des Sciences de Tunis, Laboratoire d'Analyse Math\'ematique et Applications LR11ES11, Universit\'e de Tunis El Manar, Tunis 2092, Tunisia Ecole Nationale d'Ing\'enieurs de Carthage, Universit\'e de Carthage, Tunis 2035, Tunisia

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.

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.