Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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.


Sharp results in the integral-form John–Nirenberg inequality
HTML articles powered by AMS MathViewer

by L. Slavin and V. Vasyunin PDF
Trans. Amer. Math. Soc. 363 (2011), 4135-4169 Request permission


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.
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 42A05, 42B35, 49K20
  • Retrieve articles in all journals with MSC (2010): 42A05, 42B35, 49K20
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:
  • V. Vasyunin
  • Affiliation: St. Petersburg Department of the V. A. Steklov Mathematical Institute, Russian Academy of Sciences, St. Petersburg, Russia
  • Email:
  • 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:
  • MathSciNet review: 2792983