Sharp L^p estimates on BMO
Leonid SlavinV. Vasyunin
42A0542B3549K20BMOnorm equivalenceexplicit Bellman functionMonge-Ampere equation
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.
Indiana University Mathematics Journal
2012
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10.1512/iumj.2012.61.4651
10.1512/iumj.2012.61.4651
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Indiana Univ. Math. J. 61 (2012) 1051 - 1110
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