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On the maximal function for the generalized Ornstein-Uhlenbeck semigroup

Jorge Betancor·Liliana Forzani·Roberto Scotto·Wilfredo Urbina
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Abstract

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

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Jorge Betancor, Liliana Forzani, Roberto Scotto, Wilfredo Urbina. 2006-09-30. On the maximal function for the generalized Ornstein-Uhlenbeck semigroup. https://arxiv.org/abs/math/0610011

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