Extremizers and Bellman function for martingale weak type inequality
Classical Analysis and ODEs
2013-11-12 v1 Analysis of PDEs
Abstract
We give an exact formula for the Bellman function of the weak type of martingale transform. We also give the extremal functions (actually extremal sequences of functions). We find them using the precise form of the Bellman function. The extremal examples have a fractal nature as it often happens in that kind of problems. This article is devoted to the unweighted weak type estimate.
Cite
@article{arxiv.1311.2133,
title = {Extremizers and Bellman function for martingale weak type inequality},
author = {Alexander Reznikov and Vasiliy Vasyunin and Alexander Volberg},
journal= {arXiv preprint arXiv:1311.2133},
year = {2013}
}