Monotonic rearrangements of functions with small mean oscillation
Volume 231 / 2015
Studia Mathematica 231 (2015), 257-267
MSC: Primary 42B35; Secondary 52A10, 60G46.
DOI: 10.4064/sm8326-2-2016
Published online: 26 February 2016
Abstract
We obtain sharp bounds for the monotonic rearrangement operator from “dyadic-type” classes to “continuous” ones; in particular, for the BMO space and Muckenhoupt classes. The idea is to connect the problem with a simple geometric construction named $\alpha $-extension.
