Commutators of BMO functions and singular integral operators with non-smooth kernels on spaces of Homogeneous type of finite measure

Donggao G. Deng; Yanbo B. Xu; Lixin Y. Yan

doi:10.1007/BF03218697

Commutators of BMO functions and singular integral operators with non-smooth kernels on spaces of Homogeneous type of finite measure

Donggao G. Deng, Yanbo B. Xu, Lixin Y. Yan

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

Abstract

Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on L^p(X), 1 < p < ∞. We give a sufficient condition on the kernel k(x, y) of T so that when a function b ε BMO (X), the commutator [b, T] (f) = T (bf) - bT (f) is bounded on spaces L^p for all p, 1< p < ∞.

Original language	English
Pages (from-to)	41-55
Number of pages	15
Journal	Analysis in Theory and Applications
Volume	22
Issue number	1
DOIs	https://doi.org/10.1007/BF03218697
Publication status	Published - Mar 2006

Keywords

BMO function
Commutator
homogeneous space
singular integral operator

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10.1007/BF03218697

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abstract = "Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on Lp(X), 1 < p < ∞. We give a sufficient condition on the kernel k(x, y) of T so that when a function b ε BMO (X), the commutator [b, T] (f) = T (bf) - bT (f) is bounded on spaces Lp for all p, 1< p < ∞.",

keywords = "BMO function, Commutator, homogeneous space, singular integral operator",

author = "Deng, {Donggao G.} and Xu, {Yanbo B.} and Yan, {Lixin Y.}",

year = "2006",

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doi = "10.1007/BF03218697",

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AU - Deng, Donggao G.

AU - Xu, Yanbo B.

AU - Yan, Lixin Y.

PY - 2006/3

Y1 - 2006/3

N2 - Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on Lp(X), 1 < p < ∞. We give a sufficient condition on the kernel k(x, y) of T so that when a function b ε BMO (X), the commutator [b, T] (f) = T (bf) - bT (f) is bounded on spaces Lp for all p, 1< p < ∞.

AB - Let X be a space of homogeneous type with finite measure. Let T be a singular integral operator which is bounded on Lp(X), 1 < p < ∞. We give a sufficient condition on the kernel k(x, y) of T so that when a function b ε BMO (X), the commutator [b, T] (f) = T (bf) - bT (f) is bounded on spaces Lp for all p, 1< p < ∞.

KW - BMO function

KW - Commutator

KW - homogeneous space

KW - singular integral operator

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JO - Analysis in Theory and Applications

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ER -

Commutators of BMO functions and singular integral operators with non-smooth kernels on spaces of Homogeneous type of finite measure

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