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Transactions of the American Mathematical Society

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


Authors: Yong Ding and Xudong Lai
Journal: Trans. Amer. Math. Soc. 371 (2019), 1649-1675
MSC (2010): Primary 42B15, 42B20
DOI: https://doi.org/10.1090/tran/7346
Published electronically: September 20, 2018
MathSciNet review: 3894030
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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 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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Additional Information

Yong Ding
Affiliation: Laboratory of Mathematics and Complex Systems (BNU), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China
Email: dingy@bnu.edu.cn

Xudong Lai
Affiliation: Institute for Advanced Study in Mathematics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China – and – Laboratory of Mathematics and Complex Systems (BNU), School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, People’s Republic of China
Email: xudonglai@mail.bnu.edu.cn

DOI: https://doi.org/10.1090/tran/7346
Keywords: Weak type (1, 1), criterion, singular integral operator, rough kernel
Received by editor(s): November 4, 2016
Received by editor(s) in revised form: June 21, 2017
Published electronically: September 20, 2018
Additional Notes: The first author was supported by NSFC (No. 11471033, No. 11571160, No. 11871096), and the Fundamental Research Funds for the Central Universities (No. 2014KJJCA10). The second author was supported by China Postdoctoral Science Foundation (No. 2017M621253, No. 2018T110279), the National Natural Science Foundation of China (No. 11801118) and the Fundamental Research Funds for the Central Universities.
The second author is the corresponding author.
Article copyright: © Copyright 2018 American Mathematical Society