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Dyadic John–Nirenberg space

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  17 November 2021

Juha Kinnunen  and
Kim Myyryläinen Open the ORCID record for Kim Myyryläinen [Opens in a new window]
Juha Kinnunen
Affiliation:
Department of Mathematics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland (juha.k.kinnunen@aalto.fi, kim.myyrylainen@aalto.fi)
Kim Myyryläinen
Affiliation:
Department of Mathematics, Aalto University, P.O. Box 11100, FI-00076 Aalto, Finland (juha.k.kinnunen@aalto.fi, kim.myyrylainen@aalto.fi)
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Abstract

We discuss the dyadic John–Nirenberg space that is a generalization of functions of bounded mean oscillation. A John–Nirenberg inequality, which gives a weak type estimate for the oscillation of a function, is discussed in the setting of medians instead of integral averages. We show that the dyadic maximal operator is bounded on the dyadic John–Nirenberg space and provide a method to construct nontrivial functions in the dyadic John–Nirenberg space. Moreover, we prove that the John–Nirenberg space is complete. Several open problems are also discussed.

Keywords

John–Nirenberg spacedyadicmaximal functionmedianJohn–Nirenberg inequality

MSC classification

Primary: 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 42B35: Function spaces arising in harmonic analysis
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 1 , February 2023 , pp. 1 - 18
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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