Heat-diffusion maximal operators for Laguerre semigroups with negative parameters

摘要

We prove L-P boundedness for the maximal operator of the heat semigroup associated to the Laguerre functions, {L-k(x)}(k), when the parameter a is greater than -1. Namely, the maximal operator is of strong type (p, p) if p > 1 and 2/2+alpha < p < 2/-alpha, when -1 < alpha < 0. If alpha > 0 there is strong type for 1 < p < infinity. The behavior at the end points is studied in detail. (c) 2005 Elsevier Inc. All rights reserved.