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Article overview
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Inequalities for BMO on $alpha$-trees | Leonid Slavin
; Vasily Vasyunin
; | Date: |
31 Dec 2014 | 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. | Source: | arXiv, 1501.0097 | Services: | Forum | Review | PDF | Favorites |
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