arXiv math/06100112006-10math.CAmath.AP

On the maximal function for the generalized Ornstein-Uhlenbeck semigroup

Jorge Betancor, Liliana Forzani, Roberto Scotto, Wilfredo Urbina

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

英文摘要：

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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