Sharp L^p estimates on BMO
Classical Analysis and ODEs
2011-10-11 v1
Abstract
We construct the upper and lower Bellman functions for the (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.
Cite
@article{arxiv.1110.1771,
title = {Sharp L^p estimates on BMO},
author = {Leonid Slavin and Vasily Vasyunin},
journal= {arXiv preprint arXiv:1110.1771},
year = {2011}
}
Comments
42 pages, 12 figures