The Bellman Function for a Parametric Family of Extremal Problems in BMO

Аннотация

Let I be an interval of the real line and 〈⋅〉_I be the corresponding integral average. We describe the behavior of the Bellman function for the functional F(φ) = 〈f ∘ φ〉_I, φ ∈ BMO(I), as f ranges over some parametric family of functions. Thereby, we once again demonstrate the power of the methods developed recently by V. I. Vasyunin, P. B. Zatitskiy, P. Ivanishvili, D. M. Stolyarov, and the author.