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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A maximal function characterization of the Hardy space for the Gauss measure
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by Giancarlo Mauceri, Stefano Meda and Peter Sjögren PDF
Proc. Amer. Math. Soc. 141 (2013), 1679-1692 Request permission


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 $1<p\le \infty$.
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Additional Information
  • Giancarlo Mauceri
  • Affiliation: Dipartimento di Matematica, Università di Genova, via Dodecaneso 35, 16146 Genova, Italia
  • Email:
  • Stefano Meda
  • Affiliation: Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, via R. Cozzi 53, 20125 Milano, Italy
  • Email:
  • Peter Sjögren
  • Affiliation: Mathematical Sciences, University of Gothenburg, Box 100, S-405 30 Gothenburg, Sweden — and — Mathematical Sciences, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
  • Email:
  • Received by editor(s): February 10, 2011
  • Received by editor(s) in revised form: September 7, 2011
  • Published electronically: November 2, 2012
  • Additional Notes: This work was partially supported by PRIN 2009 “Analisi Armonica”.
  • Communicated by: Michael T. Lacey
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 1679-1692
  • MSC (2010): Primary 42B30, 42B35; Secondary 42C10
  • DOI:
  • MathSciNet review: 3020855