Variational inequalities for the commutators of rough operators with BMO functions

Yanping Chen; Yong Ding; Guixiang Hong; Honghai Liu

doi:10.1007/s11425-019-1713-x

Variational inequalities for the commutators of rough operators with BMO functions

Yanping Chen^*
, Yong Ding
, Guixiang Hong
, Honghai Liu

^*Corresponding author for this work

University of Science and Technology Beijing
Beijing Normal University
Wuhan University
Henan Polytechnic University

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

15 Scopus citations

Abstract

Starting with the relatively simple observation that the variational estimates of the commutators of the standard Calderón-Zygmund operators with the bounded mean oscillation (BMO) functions can be obtained from their weighted variational estimates, we establish similar variational estimates for the commutators of the BMO functions with rough singular integrals, which do not admit any weighted variational estimates. The proof involves several Littlewood-Paley-type inequalities with the commutators as well as Bony decomposition and related para-product estimates.

Original language	English
Pages (from-to)	2437-2460
Number of pages	24
Journal	Science China Mathematics
Volume	64
Issue number	11
DOIs	https://doi.org/10.1007/s11425-019-1713-x
State	Published - Nov 2021
Externally published	Yes

Keywords

42B20
42B25
46E30
averaging operator
commutator
rough kernel
singular integral
variational inequality

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10.1007/s11425-019-1713-x

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title = "Variational inequalities for the commutators of rough operators with BMO functions",

abstract = "Starting with the relatively simple observation that the variational estimates of the commutators of the standard Calder{\'o}n-Zygmund operators with the bounded mean oscillation (BMO) functions can be obtained from their weighted variational estimates, we establish similar variational estimates for the commutators of the BMO functions with rough singular integrals, which do not admit any weighted variational estimates. The proof involves several Littlewood-Paley-type inequalities with the commutators as well as Bony decomposition and related para-product estimates.",

keywords = "42B20, 42B25, 46E30, averaging operator, commutator, rough kernel, singular integral, variational inequality",

author = "Yanping Chen and Yong Ding and Guixiang Hong and Honghai Liu",

note = "Publisher Copyright: {\textcopyright} 2021, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2021",

month = nov,

doi = "10.1007/s11425-019-1713-x",

language = "英语",

volume = "64",

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journal = "Science China Mathematics",

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}

TY - JOUR

T1 - Variational inequalities for the commutators of rough operators with BMO functions

AU - Chen, Yanping

AU - Ding, Yong

AU - Hong, Guixiang

AU - Liu, Honghai

PY - 2021/11

Y1 - 2021/11

N2 - Starting with the relatively simple observation that the variational estimates of the commutators of the standard Calderón-Zygmund operators with the bounded mean oscillation (BMO) functions can be obtained from their weighted variational estimates, we establish similar variational estimates for the commutators of the BMO functions with rough singular integrals, which do not admit any weighted variational estimates. The proof involves several Littlewood-Paley-type inequalities with the commutators as well as Bony decomposition and related para-product estimates.

AB - Starting with the relatively simple observation that the variational estimates of the commutators of the standard Calderón-Zygmund operators with the bounded mean oscillation (BMO) functions can be obtained from their weighted variational estimates, we establish similar variational estimates for the commutators of the BMO functions with rough singular integrals, which do not admit any weighted variational estimates. The proof involves several Littlewood-Paley-type inequalities with the commutators as well as Bony decomposition and related para-product estimates.

KW - 42B20

KW - 42B25

KW - 46E30

KW - averaging operator

KW - commutator

KW - rough kernel

KW - singular integral

KW - variational inequality

UR - https://www.scopus.com/pages/publications/85107551917

U2 - 10.1007/s11425-019-1713-x

DO - 10.1007/s11425-019-1713-x

M3 - 文章

AN - SCOPUS:85107551917

SN - 1674-7283

VL - 64

SP - 2437

EP - 2460

JO - Science China Mathematics

JF - Science China Mathematics

IS - 11

ER -

Variational inequalities for the commutators of rough operators with BMO functions

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Keywords

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