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Monotonic rearrangements of functions with small mean oscillation

Volume 231 / 2015

Dmitriy M. Stolyarov, Vasily I. Vasyunin, Pavel B. Zatitskiy Studia Mathematica 231 (2015), 257-267 MSC: Primary 42B35; Secondary 52A10, 60G46. DOI: 10.4064/sm8326-2-2016 Published online: 26 February 2016

Abstract

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.

Authors

  • Dmitriy M. StolyarovInstitute 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
    http://www.chebyshev.spb.ru/DmitriyStolyarov
    e-mail
    e-mail
  • Vasily I. VasyuninSt. Petersburg Department
    of Steklov Mathematical Institute
    Russian Academy of Sciences (PDMI RAS)
    27, Fontanka St.
    191023 St. Petersburg, Russia
    e-mail
  • Pavel B. ZatitskiyChebyshev 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
    http://www.chebyshev.spb.ru/pavelzatitskiy
    e-mail

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