Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Boundedness of operators on Hardy spaces via atomic decompositions
HTML articles powered by AMS MathViewer

by Marcin Bownik PDF
Proc. Amer. Math. Soc. 133 (2005), 3535-3542 Request permission

Abstract:

An example of a linear functional defined on a dense subspace of the Hardy space $H^1(\mathbb {R}^n)$ is constructed. It is shown that despite the fact that this functional is uniformly bounded on all atoms, it does not extend to a bounded functional on the whole $H^1$. Therefore, this shows that in general it is not enough to verify that an operator or a functional is bounded on atoms to conclude that it extends boundedly to the whole space. The construction is based on the fact due to Y. Meyer which states that quasi-norms corresponding to finite and infinite atomic decompositions in $H^p$, $0<p \le 1$, are not equivalent.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42B30
  • Retrieve articles in all journals with MSC (2000): 42B30
Additional Information
  • Marcin Bownik
  • Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403–1222
  • MR Author ID: 629092
  • Email: mbownik@uoregon.edu
  • Received by editor(s): July 8, 2004
  • Published electronically: June 6, 2005
  • Additional Notes: The author was partially supported by NSF grant DMS-0441817
  • Communicated by: Andreas Seeger
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 3535-3542
  • MSC (2000): Primary 42B30
  • DOI: https://doi.org/10.1090/S0002-9939-05-07892-5
  • MathSciNet review: 2163588