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arXiv · 1506.00502

Monotonic rearrangements of functions with small mean oscillation

Dmitriy M. Stolyarov·Vasily I. Vasyunin·Pavel B. Zatitskiy
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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.

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Dmitriy M. Stolyarov, Vasily I. Vasyunin, Pavel B. Zatitskiy. 2015-06-01. Monotonic rearrangements of functions with small mean oscillation. https://arxiv.org/abs/1506.00502

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