On the maximal function for the generalized Ornstein-Uhlenbeck semigroup
Jorge Betancor, Liliana Forzani, Roberto Scotto, Wilfredo Urbina
Abstract
In this note we consider the maximal function for the generalized Ornstein-Uhlenbeck semigroup in associated with the generalized Hermite polynomials \Hnμ\ and prove that it is weak type (1,1) with respect to dλμ(x) = |x|2μe-|x|2 dx, for μ>-1/2 as well as bounded on Lp(dλμ) for p>1
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