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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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Characterizing strong estimates
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by Chaoyuan Liu and Joseph Rosenblatt PDF
Proc. Amer. Math. Soc. 136 (2008), 557-567 Request permission


We describe necessary and sufficient conditions for square functions to map $L^\infty$ to $L^\infty$ for ergodic averages and Lebesgue derivatives.
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Additional Information
  • Chaoyuan Liu
  • Affiliation: Department of Mathematics and Statistics, Wallace 313, Eastern Kentucky University, Richmond, Kentucky 40475
  • Email:
  • Joseph Rosenblatt
  • Affiliation: Department of Mathematics, University of Illinois at Champaign-Urbana, 1409 W. Green Street, Urbana, Illinois 61801-2975
  • MR Author ID: 150595
  • Email:
  • Received by editor(s): October 5, 2006
  • Published electronically: October 24, 2007
  • Additional Notes: The second author recognizes the support of the NSF during the preparation of this article.
  • Communicated by: Jane M. Hawkins
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 557-567
  • MSC (2000): Primary 37A05, 37A50, 26A45; Secondary 28D05
  • DOI:
  • MathSciNet review: 2358496