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$ L^p$ bounds for the commutators of singular integrals and maximal singular integrals with rough kernels


Authors: Yanping Chen and Yong Ding
Journal: Trans. Amer. Math. Soc. 367 (2015), 1585-1608
MSC (2010): Primary 42B20, 42B25, 42B99
DOI: https://doi.org/10.1090/S0002-9947-2014-06069-8
Published electronically: July 29, 2014
MathSciNet review: 3286493
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Abstract: The commutator of convolution type Calderon-Zygmund singular integral operators with rough kernels $ p.v. \frac {\Omega (x)}{\vert x\vert^n}$ are studied. The authors established the $ L^p\,(1<p<\infty ) $ boundedness of the commutators of singular integrals and maximal singular integrals with the kernel condition which is different from the condition $ \Omega \in H^1(S^{n-1}).$


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Additional Information

Yanping Chen
Affiliation: Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, The People’s Republic of China
Email: yanpingch@126.com

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

DOI: https://doi.org/10.1090/S0002-9947-2014-06069-8
Keywords: Commutator, singular integral, maximal singular integral, rough kernel, BMO, Bony paraproduct
Received by editor(s): May 11, 2012
Received by editor(s) in revised form: December 2, 2012
Published electronically: July 29, 2014
Additional Notes: The research was supported by NSF of China (Grant: 10901017, 11371057), NCET of China (Grant: NCET-11-0574), the Fundamental Research Funds for the Central Universities (FRF-TP-12-006B) and SRFDP of China (Grant: 20130003110003)
The first author is the corresponding author
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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