Research output: Contribution to journal › Article › peer-review
We develop a general method for obtaining sharp integral estimates on BMO. Each such estimate gives rise to a Bellman function, and we show that for a large class of integral functionals, this function is a solution of a homogeneous Monge-Ampere boundary-value problem on a parabolic plane domain. Furthermore, we elaborate an essentially geometric algorithm for solving this boundary-value problem. This algorithm produces the exact Bellman function of the problem along with the optimizers in the inequalities being proved. The method presented subsumes several previous Bellman-function results for BMO, including the sharp John-Nirenberg inequality and sharp estimates of L-p-norms of BMO functions.
Original language | English |
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Pages (from-to) | 3415-3468 |
Number of pages | 54 |
Journal | Transactions of the American Mathematical Society |
Volume | 368 |
Issue number | 5 |
DOIs | |
State | Published - May 2016 |
ID: 7581894