Dyadic John-Nirenberg space

Juha Kinnunen; Kim Myyryläinen

doi:10.1017/prm.2021.66

Dyadic John-Nirenberg space

Juha Kinnunen, Kim Myyryläinen

Department of Mathematics and Systems Analysis

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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.

Original language	English
Number of pages	18
Journal	PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A: MATHEMATICS
DOIs	https://doi.org/10.1017/prm.2021.66
Publication status	E-pub ahead of print - 2021
MoE publication type	A1 Journal article-refereed

Keywords

dyadic
John-Nirenberg inequality
John-Nirenberg space
maximal function
median

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10.1017/prm.2021.66

https://arxiv.org/abs/2107.00492

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title = "Dyadic John-Nirenberg space",

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. ",

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author = "Juha Kinnunen and Kim Myyryl{\"a}inen",

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AB - 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.

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Dyadic John-Nirenberg space

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