On the maximal function for the generalized Ornstein-Uhlenbeck semigroup

LILIANA FORZANI; URBINA, W.; SCOTTO, R.; BETANCOR, J.

Quaestiones Mathematicae

Año: 2007 vol. 30 p. 471 - 482

 In this note we consider the maximal function for the generalized Ornstein-Uhlenbeck semigroup in R associated with the generalized Hermite polynomials {Hì n} and prove that it is weak type (1,1) with respect to Ornstein-Uhlenbeck semigroup in R associated with the generalized Hermite polynomials {Hì n} and prove that it is weak type (1,1) with respect to polynomials {Hì n} and prove that it is weak type (1,1) with respect to n} and prove that it is weak type (1,1) with respect to dì(x) = |x|2ìe−|x|2ì(x) = |x|2ìe−|x|2 dx, for ì > −1/2 as well as bounded on Lp(dì) forfor ì > −1/2 as well as bounded on Lp(dì) for p > 1.1.