We construct the upper and lower Bellman functions for the Lp (quasi)-norms of BMOfunctions. 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.
Original language | English |
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Pages (from-to) | 1051-1110 |
Number of pages | 60 |
Journal | Indiana University Mathematics Journal |
Volume | 61 |
Issue number | 3 |
DOIs | |
State | Published - 1 Dec 2012 |
ID: 49879026