Theory of locally concave functions and its applications to sharp estimates of integral functionals

We prove a duality theorem the computation of certain Bellman functions is usually based on. As a byproduct, we obtain sharp results about the norms of monotonic rearrangements. The main novelty of our approach is a special class of martingales and an extremal problem on this class, which is dual to...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2016-03, Vol.291, p.228-273
Main Authors: Stolyarov, D.M., Zatitskiy, P.B.
Format: Article
Language:English
Subjects:
Bellman function
BMO
Integral functional
Monotonic rearrangement
Muckenhoupt class
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Summary:We prove a duality theorem the computation of certain Bellman functions is usually based on. As a byproduct, we obtain sharp results about the norms of monotonic rearrangements. The main novelty of our approach is a special class of martingales and an extremal problem on this class, which is dual to the minimization problem for locally concave functions.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2015.11.048