On the maximal function for the generalized Ornstein-Uhlenbeck semigroup

Abstract

In this note we consider the maximal function for the generalized Ornstein-Uhlenbeck semigroup in $\RR$ associated with the generalized Hermite polynomials $\{H_n^{\mu }\}$ and prove that it is weak type (1,1) with respect to $d{\lambda }_{\mu }(x)=|x{|}^{2\mu }{e}^{-|x{|}^2}dx,$ for $\mu >-1/2$ as well as bounded on $L^p(d{\lambda }_{\mu })$ for $p>1$

10 pages. See also http://euler.ciens.ucv.ve/~wurbina/preprints.html