The space JNp: Nontriviality and duality

Galia Dafni; Tuomas Hytönen; Riikka Korte; Hong Yue

doi:10.1016/j.jfa.2018.05.007

The space JN_p: Nontriviality and duality

Galia Dafni, Tuomas Hytönen, Riikka Korte^*, Hong Yue

^*Corresponding author for this work

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Abstract

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

Original language	English
Pages (from-to)	577-603
Number of pages	27
Journal	Journal of Functional Analysis
Volume	275
Issue number	3
DOIs	https://doi.org/10.1016/j.jfa.2018.05.007
Publication status	Published - 1 Aug 2018
MoE publication type	A1 Journal article-refereed

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

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10.1016/j.jfa.2018.05.007

SCI_Dafni_Hytönen_Korte_The_Space.JNp_2018April27Accepted author manuscript, 411 KBLicence: CC BY-NC-ND

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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′ .",

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author = "Galia Dafni and Tuomas Hyt{\"o}nen and Riikka Korte and Hong Yue",

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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

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SN - 0022-1236

VL - 275

SP - 577

EP - 603

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 3

ER -

The space JN_p: Nontriviality and duality

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Keywords

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