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## Sharp estimates of integral functionals on classes of functions with small mean oscillation

Comptes Rendus Mathematique. 2015. Vol. 353. No. 12. P. 1081-1085.
Ivanishvili P., Stolyarov D., Vasyunin V., Zatitskiy P., Osipov N.N.

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 R^2). We show how the unit ball in the 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.