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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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Restricted weak type versus weak type
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by Loukas Grafakos and Mieczysław Mastyło PDF
Proc. Amer. Math. Soc. 133 (2005), 1075-1081 Request permission


We prove that translation invariant multilinear operators of restricted weak type $(1,1,\dots , 1,q)$ must necessarily be of weak type $(1,1,\dots , 1,q)$. We give applications.
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Additional Information
  • Loukas Grafakos
  • Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
  • MR Author ID: 288678
  • ORCID: 0000-0001-7094-9201
  • Email:
  • Mieczysław Mastyło
  • Affiliation: Faculty of Mathematics and Computer Science, A. Mickiewicz University – and – Institute of Mathematics, Polish Academy of Science (Poznań branch), Umultowska 87, 61-614 Poznań, Poland
  • MR Author ID: 121145
  • Email:
  • Received by editor(s): November 6, 2003
  • Published electronically: November 1, 2004
  • Additional Notes: The first author was supported by the National Science Foundation under grant DMS 0099881.
    The second author was supported by KBN Grant 1 P03A 013 26
  • Communicated by: Andreas Seeger
  • © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 1075-1081
  • MSC (2000): Primary 46B70, 42B99
  • DOI:
  • MathSciNet review: 2117208