Sharp L^p estimates on BMO

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--Ampère 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.

42 pages, 12 figures

References in corpus (1)

• Bellman functions and two weight inequalities for Haar multipliers