E. Harboure et al., On the search for weighted inequalities for operators related to the Ornstein-Uhlenbeck semigroup, MATH ANNAL, 318(2), 2000, pp. 341-353
In this paper, for each given p, 1 < p < infinity, we characterize the weig
hts v for which the centered maximal function with respect to the gaussian
measure and the Ornstein-Uhlenbeck maximal operator are well defined for ev
ery function in L-p (vd gamma) and their means converge almost everywhere.
In doing so, we find that this condition is also necessary and sufficient f
or the existence of a weight u such that the operators are bounded from L-p
(vd gamma) into L-p(ud gamma). We approach the problem by proving some vect
or valued inequalities. As a byproduct we obtain the strong type (1, 1) for
the "global" part of the centered maximal function.