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arXiv · 1412.4749

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
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Abstract

We 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.

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Paata Ivanisvili, Nikolay N. Osipov, Dmitriy M. Stolyarov, Vasily I. Vasyunin, Pavel B. Zatitskiy. 2014-12-15. Sharp estimates of integral functionals on classes of functions with small mean oscillation. https://arxiv.org/abs/1412.4749

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