On the maximal function for the generalized Ornstein-Uhlenbeck semigroup

Details On the maximal function for the generalized Ornstein-Uhlenbeck semigroup On the maximal function for the generalized Ornstein-Uhlenbeck semigroup

2006-09-30

arxiv.org/abs/math/0610011v1

Mathematics

Classical Analysis and ODEs

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

Scientific paper

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 $p>1$

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