IUMJ

Title: Sharp L^p estimates on BMO

Authors: Leonid Slavin and Vasily Vasyunin

Issue: Volume 61 (2012), Issue 3, 1051-1110

Abstract:

We construct the upper and lower Bellman functions for the $L^p$ (quasi)-norms of BMO functions. These appear as solutions to a series of Monge--Amp\`ere boundary value problems on a non-convex plane domain. The knowledge of the Bellman functions leads to sharp constants in inequalities relating average oscillations of BMO functions and various BMO norms.