Theory of locally concave functions and its applications to sharp estimates of integral functionals
Optimization and Control
2016-04-07 v1 Classical Analysis and ODEs
Probability
Abstract
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.
Keywords
Cite
@article{arxiv.1412.5350,
title = {Theory of locally concave functions and its applications to sharp estimates of integral functionals},
author = {Dmitriy M. Stolyarov and Pavel B. Zatitskiy},
journal= {arXiv preprint arXiv:1412.5350},
year = {2016}
}
Comments
37 pages, 7 figures