Heat-diffusion maximal operators for Laguerre semigroups with negative parameters

AbstractWe prove Lp boundedness for the maximal operator of the heat semigroup associated to the Laguerre functions, {Lkα}k, when the parameter α is greater than -1. Namely, the maximal operator is of strong type (p,p) if p>1 and 22+α<p<2-α, when -1<α<0. If α⩾0 there is strong type for 1