Dyadic John-Nirenberg space

Juha Kinnunen; Kim Myyryläinen

doi:10.1017/prm.2021.66

Dyadic John-Nirenberg space

Juha Kinnunen, Kim Myyryläinen

Matematiikan ja systeemianalyysin laitos

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

1 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
Sivumäärä	18
Julkaisu	PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A: MATHEMATICS
DOI - pysyväislinkit	https://doi.org/10.1017/prm.2021.66
Tila	Sähköinen julkaisu (e-pub) ennen painettua julkistusta - 2021
OKM-julkaisutyyppi	A1 Julkaistu artikkeli, soviteltu

Pääsy asiakirjaan

10.1017/prm.2021.66

https://arxiv.org/abs/2107.00492

OpenUrl-saatavuus

Koko teksti

Muut tiedostot ja linkit

Linkki julkaisuun Scopuksessa

Siteeraa tätä

@article{9b24f02204af47c3aaa79df199b5c0f3,

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. ",

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.",

year = "2021",

doi = "10.1017/prm.2021.66",

language = "English",

journal = "PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A: MATHEMATICS",

issn = "0308-2105",

publisher = "Cambridge University Press",

}

TY - JOUR

T1 - Dyadic John-Nirenberg space

AU - Kinnunen, Juha

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.

PY - 2021

Y1 - 2021

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 - http://www.scopus.com/inward/record.url?scp=85120035149&partnerID=8YFLogxK

U2 - 10.1017/prm.2021.66

DO - 10.1017/prm.2021.66

M3 - Article

AN - SCOPUS:85120035149

JO - PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A: MATHEMATICS

JF - PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A: MATHEMATICS

SN - 0308-2105

ER -

Dyadic John-Nirenberg space

Abstrakti

Pääsy asiakirjaan

OpenUrl-saatavuus

Muut tiedostot ja linkit

Sormenjälki

Siteeraa tätä