An atomic Hardy space H-1(gamma) associated to the Gauss measure gamma in R-n has been introduced by the first two authors. We first prove that it is equivalent to use (1, r)- or (1, infinity)-atoms to define this H-1(gamma). For n = 1, a maximal function characterization of H-1(gamma) is found. In arbitrary dimension, we give a description of the nonnegative functions in H-1(gamma) and use it to prove that L-p(gamma) subset of H-1(gamma) for 1 < p <= infinity
Mauceri, G., Meda, S., Sjogren, P. (2013). A maximal function characterization of the Hardy space for the Gauss measure. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 141(5), 1679-1692 [10.1090/S0002-9939-2012-11443-1].
A maximal function characterization of the Hardy space for the Gauss measure
MEDA, STEFANOSecondo
;
2013
Abstract
An atomic Hardy space H-1(gamma) associated to the Gauss measure gamma in R-n has been introduced by the first two authors. We first prove that it is equivalent to use (1, r)- or (1, infinity)-atoms to define this H-1(gamma). For n = 1, a maximal function characterization of H-1(gamma) is found. In arbitrary dimension, we give a description of the nonnegative functions in H-1(gamma) and use it to prove that L-p(gamma) subset of H-1(gamma) for 1 < p <= infinity
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