Norm Estimates and Uncertainty Principles Associated with the Laguerre Integral Transform

Abstract

In this paper we present some results concerning the action of the Laguerre integral transform over the class of polynomials and over the class of infinitely differentiable functions. We prove several uncertainty inequalities of Heisenberg-type, and we also indicate an explicit boundedness for two classes of generalized Laguerre integral transforms which include the classical Riemann Liouville fractional integral.