Geodesic
Monotonic rearrangements of functions with small mean oscillation
Dmitriy M. Stolyarov 1   ; Vasily I. Vasyunin 2   ; Pavel B. Zatitskiy 3
1 Institute of Mathematics Polish Academy of Sciences 00-656 Warszawa, Poland and Chebyshev Laboratory St. Petersburg State University 14th Line V.O., 29B 199178 St. Petersburg, Russia and St. Petersburg Department of Steklov Mathematical Institute Russian Academy of Sciences (PDMI RAS) 27, Fontanka St. 191023 St. Petersburg, Russia <a href="http://www.chebyshev.spb.ru/DmitriyStolyarov">http://www.chebyshev.spb.ru/DmitriyStolyarov</a>
2 St. Petersburg Department of Steklov Mathematical Institute Russian Academy of Sciences (PDMI RAS) 27, Fontanka St. 191023 St. Petersburg, Russia
3 Chebyshev Laboratory St. Petersburg State University 14th Line V.O., 29B 199178 St. Petersburg, Russia and St. Petersburg Department of Steklov Mathematical Institute Russian Academy of Sciences (PDMI RAS) 27, Fontanka St. 191023 St. Petersburg, Russia <a href="http://www.chebyshev.spb.ru/pavelzatitskiy">http://www.chebyshev.spb.ru/pavelzatitskiy</a>
Studia Mathematica, Tome 231 (2015) no. 3, pp. 257-267 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We obtain sharp bounds for the monotonic rearrangement operator from “dyadic-type” classes to “continuous” ones; in particular, for the BMO space and Muckenhoupt classes. The idea is to connect the problem with a simple geometric construction named $\alpha $-extension.
DOI : 10.4064/sm8326-2-2016
Keywords: obtain sharp bounds monotonic rearrangement operator dyadic type classes continuous particular bmo space muckenhoupt classes idea connect problem simple geometric construction named alpha extension

Dmitriy M. Stolyarov  1   ; Vasily I. Vasyunin  2   ; Pavel B. Zatitskiy  3

1 Institute of Mathematics Polish Academy of Sciences 00-656 Warszawa, Poland and Chebyshev Laboratory St. Petersburg State University 14th Line V.O., 29B 199178 St. Petersburg, Russia and St. Petersburg Department of Steklov Mathematical Institute Russian Academy of Sciences (PDMI RAS) 27, Fontanka St. 191023 St. Petersburg, Russia <a href="http://www.chebyshev.spb.ru/DmitriyStolyarov">http://www.chebyshev.spb.ru/DmitriyStolyarov</a>
2 St. Petersburg Department of Steklov Mathematical Institute Russian Academy of Sciences (PDMI RAS) 27, Fontanka St. 191023 St. Petersburg, Russia
3 Chebyshev Laboratory St. Petersburg State University 14th Line V.O., 29B 199178 St. Petersburg, Russia and St. Petersburg Department of Steklov Mathematical Institute Russian Academy of Sciences (PDMI RAS) 27, Fontanka St. 191023 St. Petersburg, Russia <a href="http://www.chebyshev.spb.ru/pavelzatitskiy">http://www.chebyshev.spb.ru/pavelzatitskiy</a> 
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     title = {Monotonic rearrangements of functions with small mean oscillation},
     journal = {Studia Mathematica},
     pages = {257--267},
     year = {2015},
     volume = {231},
     number = {3},
     doi = {10.4064/sm8326-2-2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm8326-2-2016/}
}
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Dmitriy M. Stolyarov; Vasily I. Vasyunin; Pavel B. Zatitskiy. Monotonic rearrangements of functions with small mean oscillation. Studia Mathematica, Tome 231 (2015) no. 3, pp. 257-267. doi: 10.4064/sm8326-2-2016

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