Weighted norm inequalities for heat-diffusion Laguerre's semigroups

Abstract

We consider three systems of Laguerre functions and their corresponding heat diffusion semigroups. For the associate maximal operators, we give necessary and sufficient conditions in order to obtain strong type, weak type and restricted weak type (p,p), with respect to a power weight x δ, for 1 ≤ p ≤ ∞. We also obtain sufficient conditions for more general weights.