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# A maximal function characterization of the Hardy space for the Gauss measure

Giancarlo Mauceri ; Stefano Meda ; Peter Sjögren (Institutionen för matematiska vetenskaper, matematik)
Proceedings of the American Mathematical Society (1088-6826). Vol. 141 (2013), 5, p. 1679-1692.

An atomic Hardy space $H^1(\gamma )$ associated to the Gauss measure $\gamma$ in $\mathbb{R}^n$ has been introduced by the first two authors. We first prove that it is equivalent to use $(1,r)$- or $(1,\infty )$-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 $L^p(\gamma )\subset H^1(\gamma )$ for \$ 1

CPL Pubid: 129942

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Institutionen för matematiska vetenskaper, matematik (2005-2016)