Reduction of calderón commutators

Paul S. Muhly; Jingbo Xia

doi:10.1112/S002460939700369X

Reduction of calderón commutators

Paul S. Muhly
, Jingbo Xia

Mathematics

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

1 Scopus citations

Abstract

Let A₁,..., A_n be Lipschitz functions on R such that A′₁, ... , A′_n ∈ VMO. We show that on any bounded interval, the Calderon commutator associated with the kernel (A₁(x)-A₁(y))...(A_n(x)-A _n(y))/(x-y)ⁿ⁺¹ is a compact perturbation of -πiHM _{A′1...A′n}, where H is the Hilbert transform.

Original language	English
Pages (from-to)	67-72
Number of pages	6
Journal	Bulletin of the London Mathematical Society
Volume	30
Issue number	1
DOIs	https://doi.org/10.1112/S002460939700369X
State	Published - Jan 1998

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title = "Reduction of calder{\'o}n commutators",

abstract = "Let A1,..., An be Lipschitz functions on R such that A′1, ... , A′n ∈ VMO. We show that on any bounded interval, the Calderon commutator associated with the kernel (A1(x)-A1(y))...(An(x)-A n(y))/(x-y)n+1 is a compact perturbation of -πiHM A′1...A′n, where H is the Hilbert transform.",

author = "Muhly, \{Paul S.\} and Jingbo Xia",

year = "1998",

month = jan,

doi = "10.1112/S002460939700369X",

language = "English",

volume = "30",

pages = "67--72",

journal = "Bulletin of the London Mathematical Society",

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publisher = "John Wiley and Sons Ltd",

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T1 - Reduction of calderón commutators

AU - Muhly, Paul S.

AU - Xia, Jingbo

PY - 1998/1

Y1 - 1998/1

N2 - Let A1,..., An be Lipschitz functions on R such that A′1, ... , A′n ∈ VMO. We show that on any bounded interval, the Calderon commutator associated with the kernel (A1(x)-A1(y))...(An(x)-A n(y))/(x-y)n+1 is a compact perturbation of -πiHM A′1...A′n, where H is the Hilbert transform.

AB - Let A1,..., An be Lipschitz functions on R such that A′1, ... , A′n ∈ VMO. We show that on any bounded interval, the Calderon commutator associated with the kernel (A1(x)-A1(y))...(An(x)-A n(y))/(x-y)n+1 is a compact perturbation of -πiHM A′1...A′n, where H is the Hilbert transform.

UR - https://www.scopus.com/pages/publications/0031987004

U2 - 10.1112/S002460939700369X

DO - 10.1112/S002460939700369X

M3 - Article

AN - SCOPUS:0031987004

SN - 0024-6093

VL - 30

SP - 67

EP - 72

JO - Bulletin of the London Mathematical Society

JF - Bulletin of the London Mathematical Society

IS - 1

ER -

Reduction of calderón commutators

Abstract

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