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

^*Tämän työn vastaava kirjoittaja

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

30 Sitaatiot (Scopus)

81 Lataukset (Pure)

Abstrakti

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^′.

Alkuperäiskieli	Englanti
Sivut	577-603
Sivumäärä	27
Julkaisu	Journal of Functional Analysis
Vuosikerta	275
Numero	3
DOI - pysyväislinkit	https://doi.org/10.1016/j.jfa.2018.05.007
Tila	Julkaistu - 1 elok. 2018
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Pääsy asiakirjaan

10.1016/j.jfa.2018.05.007

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

Muut tiedostot ja linkit

Link to publication in Scopus

Siteeraa tätä

@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 = aug,

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",

publisher = "Elsevier",

number = "3",

}

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

AN - SCOPUS:85047228658

SN - 0022-1236

VL - 275

SP - 577

EP - 603

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 3

ER -