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arXiv · 1110.1771

Sharp L^p estimates on BMO

Leonid Slavin·Vasily Vasyunin
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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.

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Leonid Slavin, Vasily Vasyunin. 2011-10-08. Sharp L^p estimates on BMO. https://arxiv.org/abs/1110.1771

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