We consider the strong form of the John-Nirenberg inequality for the L2-based BMO. We construct explicit Bellman functions for the inequality in the continuous and dyadic settings and obtain the sharp constant, as well as the precise bound on the inequality's range of validity, both previously unknown. The results for the two cases are substantially different. The paper not only gives another instance in the short list of such explicit calculations, but also presents the Bellman function method as a sequence of clear steps, adaptable to a wide variety of applications.
Original language | English |
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Pages (from-to) | 4135-4169 |
Number of pages | 35 |
Journal | Transactions of the American Mathematical Society |
Volume | 363 |
Issue number | 8 |
DOIs | |
State | Published - 1 Aug 2011 |
ID: 49879215