Weak type (1,1) bound criterion for singular integrals with rough kernel and its applications

Yong Ding; Xudong Lai

doi:10.1090/tran/7346

Weak type (1,1) bound criterion for singular integrals with rough kernel and its applications

Yong Ding
, Xudong Lai

School of Mathematics

Beijing Normal University

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

22 Scopus citations

Abstract

In this paper, a weak type (1,1) bound criterion is established for singular integral operators with rough kernel. As some applications of this criterion, we show that some important operators with rough kernel in harmonic analysis, such as the Calderón commutator, the higher order Calderón commutator, the general Calderón commutator, the Calderón commutator of Bajsanski–Coifman type, and the general singular integral of Muckenhoupt type, are all of weak type (1,1).

Original language	English
Pages (from-to)	1649-1675
Number of pages	27
Journal	Transactions of the American Mathematical Society
Volume	371
Issue number	3
DOIs	https://doi.org/10.1090/tran/7346
State	Published - 2019

Keywords

Criterion
Rough kernel
Singular integral operator
Weak type (1,1)

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abstract = "In this paper, a weak type (1,1) bound criterion is established for singular integral operators with rough kernel. As some applications of this criterion, we show that some important operators with rough kernel in harmonic analysis, such as the Calder{\'o}n commutator, the higher order Calder{\'o}n commutator, the general Calder{\'o}n commutator, the Calder{\'o}n commutator of Bajsanski–Coifman type, and the general singular integral of Muckenhoupt type, are all of weak type (1,1).",

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AB - In this paper, a weak type (1,1) bound criterion is established for singular integral operators with rough kernel. As some applications of this criterion, we show that some important operators with rough kernel in harmonic analysis, such as the Calderón commutator, the higher order Calderón commutator, the general Calderón commutator, the Calderón commutator of Bajsanski–Coifman type, and the general singular integral of Muckenhoupt type, are all of weak type (1,1).

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KW - Rough kernel

KW - Singular integral operator

KW - Weak type (1,1)

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ER -

Weak type (1,1) bound criterion for singular integrals with rough kernel and its applications

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