Dyadic John-Nirenberg space

Juha Kinnunen; Kim Myyryläinen

doi:10.1017/prm.2021.66

Dyadic John-Nirenberg space

Juha Kinnunen
, Kim Myyryläinen

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

6 Sitaatiot (Scopus)

Abstrakti

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.

Alkuperäiskieli	Englanti
Sivut	1-18
Sivumäärä	18
Julkaisu	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Vuosikerta	153
Numero	1
Varhainen verkossa julkaisun päivämäärä	2021
DOI - pysyväislinkit	https://doi.org/10.1017/prm.2021.66
Tila	Julkaistu - 1 helmik. 2023
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Rahoitus

The research was supported by the Academy of Finland.

Pääsy asiakirjaan

10.1017/prm.2021.66

https://arxiv.org/abs/2107.00492

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keywords = "dyadic, John-Nirenberg inequality, John-Nirenberg space, maximal function, median",

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

note = "Funding Information: The research was supported by the Academy of Finland. Publisher Copyright: Copyright {\textcopyright} The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.",

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AU - Myyryläinen, Kim

N1 - Funding Information: The research was supported by the Academy of Finland. Publisher Copyright: Copyright © The Author(s), 2021. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.

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N2 - 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.

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.

KW - dyadic

KW - John-Nirenberg inequality

KW - John-Nirenberg space

KW - maximal function

KW - median

UR - https://www.scopus.com/pages/publications/85120035149

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DO - 10.1017/prm.2021.66

M3 - Article

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SN - 0308-2105

VL - 153

SP - 1

EP - 18

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

IS - 1

ER -

Dyadic John-Nirenberg space

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