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06 August 2020
 
  » arxiv » 1412.4749

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Sharp estimates of integral functionals on classes of functions with small mean oscillation
Paata Ivanisvili ; Nikolay N. Osipov ; Dmitriy M. Stolyarov ; Vasily I. Vasyunin ; Pavel B. Zatitskiy ;
Date 15 Dec 2014
AbstractWe unify several Bellman function problems into one setting. For that purpose we define a class of functions that have, in a sense, small mean oscillation (this class depends on two convex sets in $mathbb{R}^2$). We show how the unit ball in the $mathrm{BMO}$ space, or a Muckenhoupt class, or a Gehring class can be described in such a fashion. Finally, we consider a Bellman function problem on these classes, discuss its solution and related questions.
Source arXiv, 1412.4749
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