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A maximal function characterization of the Hardy space for the Gauss measure
Journal article, 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

## Author

### Giancarlo Mauceri

### Stefano Meda

### Peter Sjögren

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

#### Proceedings of the American Mathematical Society

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

Vol. 141 5 1679-1692### Subject Categories

Mathematical Analysis

### DOI

10.1090/S0002-9939-2012-11443-1