L2 boundedness of commutators of Calderón-Zygmund singular integral operators

Donggao Deng; Lixin Yan; Qixiang Yang

L2 boundedness of commutators of Calderón-Zygmund singular integral operators

Donggao Deng^*, Lixin Yan, Qixiang Yang

^*Corresponding author for this work

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

6 Citations (Scopus)

Abstract

L² boundedness of commutators of Calderón-Zygmund singular integral operators with weak kernel [b, T]f= bTf - T(bf) is proved when 6 ∈ BMO. This result extends Coifman-Rochberg-Weiss Theorem. An equivalent version is that bilinear operator gT( f) -fT * ( g ) ∈ H¹, provided f, g ∈ L². This is a new result in the compensated compactness theory.

Original language	English
Pages (from-to)	426-427
Number of pages	2
Journal	Progress in Natural Science
Volume	8
Issue number	4
Publication status	Published - 1998

Keywords

BCR algorithm
BMO
Commutator
Hardy space
Singular integral
Wavelets

Cite this

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title = "L2 boundedness of commutators of Calder{\'o}n-Zygmund singular integral operators",

abstract = "L2 boundedness of commutators of Calder{\'o}n-Zygmund singular integral operators with weak kernel [b, T]f= bTf - T(bf) is proved when 6 ∈ BMO. This result extends Coifman-Rochberg-Weiss Theorem. An equivalent version is that bilinear operator gT( f) -fT * ( g ) ∈ H1, provided f, g ∈ L2. This is a new result in the compensated compactness theory.",

keywords = "BCR algorithm, BMO, Commutator, Hardy space, Singular integral, Wavelets",

author = "Donggao Deng and Lixin Yan and Qixiang Yang",

year = "1998",

language = "English",

volume = "8",

pages = "426--427",

journal = "Progress in Natural Science",

issn = "1002-0071",

publisher = "Elsevier",

number = "4",

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T1 - L2 boundedness of commutators of Calderón-Zygmund singular integral operators

AU - Deng, Donggao

AU - Yan, Lixin

AU - Yang, Qixiang

PY - 1998

Y1 - 1998

N2 - L2 boundedness of commutators of Calderón-Zygmund singular integral operators with weak kernel [b, T]f= bTf - T(bf) is proved when 6 ∈ BMO. This result extends Coifman-Rochberg-Weiss Theorem. An equivalent version is that bilinear operator gT( f) -fT * ( g ) ∈ H1, provided f, g ∈ L2. This is a new result in the compensated compactness theory.

AB - L2 boundedness of commutators of Calderón-Zygmund singular integral operators with weak kernel [b, T]f= bTf - T(bf) is proved when 6 ∈ BMO. This result extends Coifman-Rochberg-Weiss Theorem. An equivalent version is that bilinear operator gT( f) -fT * ( g ) ∈ H1, provided f, g ∈ L2. This is a new result in the compensated compactness theory.

KW - BCR algorithm

KW - BMO

KW - Commutator

KW - Hardy space

KW - Singular integral

KW - Wavelets

UR - http://www.scopus.com/inward/record.url?scp=20944442256&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:20944442256

SN - 1002-0071

VL - 8

SP - 426

EP - 427

JO - Progress in Natural Science

JF - Progress in Natural Science

IS - 4

ER -

L2 boundedness of commutators of Calderón-Zygmund singular integral operators

Abstract

Keywords

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