The Cauchy integral, bounded and compact commutators

Ji Li; Trang T. T. Nguyen; Lesley A. Ward; Brett D. Wick

doi:10.4064/sm180715-13-12

The Cauchy integral, bounded and compact commutators

Ji Li, Trang T. T. Nguyen, Lesley A. Ward, Brett D. Wick

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We study the commutator of the well-known Cauchy integral with a locally integrable function b on R, and establish a characterisation of the BMO space on R via the L^p boundedness of this commutator. Moreover, we also establish a characterisation of the VMO space on R via the compactness of this commutator.

Original language	English
Pages (from-to)	193-216
Number of pages	24
Journal	Studia Mathematica
Volume	250
Issue number	2
DOIs	https://doi.org/10.4064/sm180715-13-12
Publication status	Published - 2020

Keywords

BMO spaces
VMO spaces
commutators
Cauchy integrals

Access to Document

10.4064/sm180715-13-12

Cite this

@article{ed94c6c9076b4a38a3df41694ea3d7f1,

title = "The Cauchy integral, bounded and compact commutators",

abstract = "We study the commutator of the well-known Cauchy integral with a locally integrable function b on R, and establish a characterisation of the BMO space on R via the Lp boundedness of this commutator. Moreover, we also establish a characterisation of the VMO space on R via the compactness of this commutator.",

keywords = "BMO spaces, VMO spaces, commutators, Cauchy integrals",

author = "Ji Li and Nguyen, {Trang T. T.} and Ward, {Lesley A.} and Wick, {Brett D.}",

year = "2020",

doi = "10.4064/sm180715-13-12",

language = "English",

volume = "250",

pages = "193--216",

journal = "Studia Mathematica",

issn = "0039-3223",

publisher = "Polska Akademia Nauk",

number = "2",

}

TY - JOUR

T1 - The Cauchy integral, bounded and compact commutators

AU - Li, Ji

AU - Nguyen, Trang T. T.

AU - Ward, Lesley A.

AU - Wick, Brett D.

PY - 2020

Y1 - 2020

N2 - We study the commutator of the well-known Cauchy integral with a locally integrable function b on R, and establish a characterisation of the BMO space on R via the Lp boundedness of this commutator. Moreover, we also establish a characterisation of the VMO space on R via the compactness of this commutator.

AB - We study the commutator of the well-known Cauchy integral with a locally integrable function b on R, and establish a characterisation of the BMO space on R via the Lp boundedness of this commutator. Moreover, we also establish a characterisation of the VMO space on R via the compactness of this commutator.

KW - BMO spaces

KW - VMO spaces

KW - commutators

KW - Cauchy integrals

UR - http://www.scopus.com/inward/record.url?scp=85075168836&partnerID=8YFLogxK

U2 - 10.4064/sm180715-13-12

DO - 10.4064/sm180715-13-12

M3 - Article

VL - 250

SP - 193

EP - 216

JO - Studia Mathematica

JF - Studia Mathematica

SN - 0039-3223

IS - 2

ER -

The Cauchy integral, bounded and compact commutators

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this