Sharp L^p estimates on BMO

By L. Slavin, V. Vasyunin. 2011

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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--Ampere 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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/74d4a07cbc4897dcb4d61a4ae6e720b114c098f6