The John–Nirenberg Space: Equality of the Vanishing Subspaces VJNp and CJNp

Riikka Korte; Timo Takala

doi:10.1007/s12220-023-01512-6

The John–Nirenberg Space: Equality of the Vanishing Subspaces VJN_p and CJN_p

Riikka Korte, Timo Takala^*

^*Tämän työn vastaava kirjoittaja

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

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46 Lataukset (Pure)

Abstrakti

The John–Nirenberg spaces JN_p are generalizations of the space of bounded mean oscillation BMO with JN_∞= BMO . Their vanishing subspaces VJN_p and CJN_p are defined in similar ways as VMO and CMO, which are subspaces of BMO. As our main result, we prove that VJN_p and CJN_p coincide by showing that certain Morrey type integrals of JN_p functions tend to zero for small and large cubes. We also show that JN_p_,_q(Rⁿ) = L^p(Rⁿ) / R , if p= q .

Alkuperäiskieli	Englanti
Artikkeli	67
Sivut	1-19
Sivumäärä	19
Julkaisu	Journal of Geometric Analysis
Vuosikerta	34
Numero	3
DOI - pysyväislinkit	https://doi.org/10.1007/s12220-023-01512-6
Tila	Julkaistu - maalisk. 2024
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Pääsy asiakirjaan

10.1007/s12220-023-01512-6Lisenssi: CC BY

The John–Nirenberg SpaceFinal published version, 411 KBLisenssi: CC BY

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title = "The John–Nirenberg Space: Equality of the Vanishing Subspaces VJNp and CJNp",

abstract = "The John–Nirenberg spaces JNp are generalizations of the space of bounded mean oscillation BMO with JN∞= BMO . Their vanishing subspaces VJNp and CJNp are defined in similar ways as VMO and CMO, which are subspaces of BMO. As our main result, we prove that VJNp and CJNp coincide by showing that certain Morrey type integrals of JNp functions tend to zero for small and large cubes. We also show that JNp,q(Rn) = Lp(Rn) / R , if p= q .",

keywords = "Bounded mean oscillation, Euclidean space, John–Nirenberg inequality, John–Nirenberg space, Morrey type integral, Vanishing subspace",

author = "Riikka Korte and Timo Takala",

note = "Publisher Copyright: {\textcopyright} 2024, The Author(s).",

year = "2024",

month = mar,

doi = "10.1007/s12220-023-01512-6",

language = "English",

volume = "34",

pages = "1--19",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

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TY - JOUR

T1 - The John–Nirenberg Space

T2 - Equality of the Vanishing Subspaces VJNp and CJNp

AU - Korte, Riikka

AU - Takala, Timo

PY - 2024/3

Y1 - 2024/3

N2 - The John–Nirenberg spaces JNp are generalizations of the space of bounded mean oscillation BMO with JN∞= BMO . Their vanishing subspaces VJNp and CJNp are defined in similar ways as VMO and CMO, which are subspaces of BMO. As our main result, we prove that VJNp and CJNp coincide by showing that certain Morrey type integrals of JNp functions tend to zero for small and large cubes. We also show that JNp,q(Rn) = Lp(Rn) / R , if p= q .

AB - The John–Nirenberg spaces JNp are generalizations of the space of bounded mean oscillation BMO with JN∞= BMO . Their vanishing subspaces VJNp and CJNp are defined in similar ways as VMO and CMO, which are subspaces of BMO. As our main result, we prove that VJNp and CJNp coincide by showing that certain Morrey type integrals of JNp functions tend to zero for small and large cubes. We also show that JNp,q(Rn) = Lp(Rn) / R , if p= q .

KW - Bounded mean oscillation

KW - Euclidean space

KW - John–Nirenberg inequality

KW - John–Nirenberg space

KW - Morrey type integral

KW - Vanishing subspace

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U2 - 10.1007/s12220-023-01512-6

DO - 10.1007/s12220-023-01512-6

M3 - Article

AN - SCOPUS:85181896318

SN - 1050-6926

VL - 34

SP - 1

EP - 19

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

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M1 - 67

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