The space JNp: Nontriviality and duality

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The space JNp : Nontriviality and duality. / Dafni, Galia; Hytönen, Tuomas; Korte, Riikka; Yue, Hong.

julkaisussa: Journal of Functional Analysis, Vuosikerta 275, Nro 3, 01.08.2018, s. 577-603.

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

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Dafni, G, Hytönen, T, Korte, R & Yue, H 2018, 'The space JNp: Nontriviality and duality' Journal of Functional Analysis, Vuosikerta. 275, Nro 3, Sivut 577-603. https://doi.org/10.1016/j.jfa.2018.05.007

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Dafni, Galia ; Hytönen, Tuomas ; Korte, Riikka ; Yue, Hong. / The space JNp : Nontriviality and duality. Julkaisussa: Journal of Functional Analysis. 2018 ; Vuosikerta 275, Nro 3. Sivut 577-603.

Bibtex - Lataa

@article{ac56061abe144202bcfce83e80700a62,
title = "The space JNp: Nontriviality and duality",
abstract = "We study a function space JNp based on a condition introduced by John and Nirenberg as a variant of BMO. It is known that Lp⊂JNp⊊Lp,∞, but otherwise the structure of JNp is largely a mystery. Our first main result is the construction of a function that belongs to JNp but not Lp, showing that the two spaces are not the same. Nevertheless, we prove that for monotone functions, the classes JNp and Lp do coincide. Our second main result describes JNp as the dual of a new Hardy kind of space HKp′ .",
keywords = "Atomic decomposition, Bounded mean oscillation, Duality, John–Nirenberg inequality, SELF-IMPROVING PROPERTIES, BOUNDED MEAN-OSCILLATION, BMO-TYPE NORMS, JOHN-NIRENBERG, POINCARE INEQUALITIES, PERIMETER, SETS",
author = "Galia Dafni and Tuomas Hyt{\"o}nen and Riikka Korte and Hong Yue",
year = "2018",
month = "8",
day = "1",
doi = "10.1016/j.jfa.2018.05.007",
language = "English",
volume = "275",
pages = "577--603",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
number = "3",

}

RIS - Lataa

TY - JOUR

T1 - The space JNp

T2 - Nontriviality and duality

AU - Dafni, Galia

AU - Hytönen, Tuomas

AU - Korte, Riikka

AU - Yue, Hong

PY - 2018/8/1

Y1 - 2018/8/1

N2 - We study a function space JNp based on a condition introduced by John and Nirenberg as a variant of BMO. It is known that Lp⊂JNp⊊Lp,∞, but otherwise the structure of JNp is largely a mystery. Our first main result is the construction of a function that belongs to JNp but not Lp, showing that the two spaces are not the same. Nevertheless, we prove that for monotone functions, the classes JNp and Lp do coincide. Our second main result describes JNp as the dual of a new Hardy kind of space HKp′ .

AB - We study a function space JNp based on a condition introduced by John and Nirenberg as a variant of BMO. It is known that Lp⊂JNp⊊Lp,∞, but otherwise the structure of JNp is largely a mystery. Our first main result is the construction of a function that belongs to JNp but not Lp, showing that the two spaces are not the same. Nevertheless, we prove that for monotone functions, the classes JNp and Lp do coincide. Our second main result describes JNp as the dual of a new Hardy kind of space HKp′ .

KW - Atomic decomposition

KW - Bounded mean oscillation

KW - Duality

KW - John–Nirenberg inequality

KW - SELF-IMPROVING PROPERTIES

KW - BOUNDED MEAN-OSCILLATION

KW - BMO-TYPE NORMS

KW - JOHN-NIRENBERG

KW - POINCARE INEQUALITIES

KW - PERIMETER

KW - SETS

UR - http://www.scopus.com/inward/record.url?scp=85047228658&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2018.05.007

DO - 10.1016/j.jfa.2018.05.007

M3 - Article

VL - 275

SP - 577

EP - 603

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 3

ER -

ID: 32108853