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- W2469636188 abstract "We develop technical tools that enable the use of Bellman functions for BMO defined on $alpha$-trees, which are structures that generalize dyadic lattices. As applications, we prove the integral John--Nirenberg inequality and an inequality relating $L^1$- and $L^2$-oscillations for BMO on $alpha$-trees, with explicit constants. When the tree in question is the collection of all dyadic cubes in $mathbb{R}^n,$ the inequalities proved are sharp. We also reformulate the John--Nirenberg inequality for the continuous BMO in terms of special martingales generated by BMO functions. The tools presented can be used for any function class that corresponds to a non-convex Bellman domain." @default.
- W2469636188 created "2016-07-22" @default.
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- W2469636188 date "2014-12-31" @default.
- W2469636188 modified "2023-09-27" @default.
- W2469636188 title "Inequalities for BMO on $alpha$-trees" @default.
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