Monotonic rearrangements of functions with small mean oscillation

Abstract

We obtain sharp bounds for the monotonic rearrangement operator from "dyadic-type" classes to "continuous". In particular, for the $\mathrm{BMO}$ space and Muckenhoupt classes. The idea is to connect the problem with a simple geometric construction named $\alpha$-extension.

arXiv comment12 pages, 2 figures