# A maximal function characterization of the Hardy space for the Gauss measure Artikel i vetenskaplig tidskrift, 2013

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

## Författare

#### Peter Sjögren

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

#### Proceedings of the American Mathematical Society

0002-9939 (ISSN) 1088-6826 (eISSN)

Vol. 141 1679-1692

#### Ämneskategorier

Matematisk analys

#### DOI

10.1090/S0002-9939-2012-11443-1