Sharp L^p estimates on BMO

Details Sharp L^p estimates on BMO Sharp L^p estimates on BMO

2011-10-08

arxiv.org/abs/1110.1771v1

Mathematics

Classical Analysis and ODEs

42 pages, 12 figures

Scientific paper

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.

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