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The John-Nirenberg constant of $ \mathrm{BMO}^p$, $ p> 2$


Authors: L. Slavin and V. Vasyunin
Translated by: The Authors
Original publication: Algebra i Analiz, tom 28 (2016), nomer 2.
Journal: St. Petersburg Math. J. 28 (2017), 181-196
MSC (2010): Primary 42A05, 42B35, 49K20
DOI: https://doi.org/10.1090/spmj/1445
Published electronically: February 15, 2017
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Abstract: This paper is a continuation of earlier work by the first author who determined the John-Nirenberg constant of $ \mathrm {BMO}^p\big ((0,1)\big )$ for the range $ 1\le p\le 2$. Here, that constant is computed for $ p>2$. As before, the main results rely on Bellman functions for the $ L^p$ norms of the logarithms of $ A_\infty $ weights, but for $ p>2$ these functions turn out to have a significantly more complicated structure than for $ 1\le p\le 2$.


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Additional Information

L. Slavin
Affiliation: University of Cincinnati, 2815 Commons Way, Cincinnati, Ohio 45221
Email: leonid.slavin@uc.edu

V. Vasyunin
Affiliation: St. Petersburg Branch, V. A. Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, 191023, St. Petersburg, Russia; St. Petersburg State University, Universitetskii pr. 28, 198504, St. Petersburg, Russia
Email: vasyunin@pdmi.ras.ru

DOI: https://doi.org/10.1090/spmj/1445
Keywords: BMO, John--Nirenberg inequality, Bellman function
Received by editor(s): June 1, 2015
Published electronically: February 15, 2017
Additional Notes: The authors were supported by RSF (grant no. 14-41-00010)
Article copyright: © Copyright 2017 American Mathematical Society