Monotonic rearrangements of functions with small mean oscillation
classification
🧮 math.CA
math.PR
keywords
classesmonotonicalphaboundsconnectconstructioncontinuousdyadic-type
read the original 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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