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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Sharp results in the integral-form John–Nirenberg inequality
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by L. Slavin and V. Vasyunin PDF
Trans. Amer. Math. Soc. 363 (2011), 4135-4169 Request permission

Abstract:

We consider the strong form of the John-Nirenberg inequality for the $L^2\!$-based BMO. We construct explicit Bellman functions for the inequality in the continuous and dyadic settings and obtain the sharp constant, as well as the precise bound on the inequality’s range of validity, both previously unknown. The results for the two cases are substantially different. The paper not only gives another instance in the short list of such explicit calculations, but also presents the Bellman function method as a sequence of clear steps, adaptable to a wide variety of applications.
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Additional Information
  • L. Slavin
  • Affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025
  • MR Author ID: 121075
  • ORCID: 0000-0002-9502-8852
  • Email: leonid.slavin@uc.edu
  • V. Vasyunin
  • Affiliation: St. Petersburg Department of the V. A. Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, Russia
  • Email: vasyunin@pdmi.ras.ru
  • Received by editor(s): June 18, 2008
  • Received by editor(s) in revised form: May 16, 2009
  • Published electronically: March 9, 2011
  • Additional Notes: The second author’s research was supported in part by RFBR (grant no. 08-01-00723-a)
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 4135-4169
  • MSC (2010): Primary 42A05, 42B35, 49K20
  • DOI: https://doi.org/10.1090/S0002-9947-2011-05112-3
  • MathSciNet review: 2792983