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On rough singular integrals along real-analytic submanifolds

  • Feng Liu , Huoxiong Wu und Qingying Xue EMAIL logo
Veröffentlicht/Copyright: 8. November 2019

Abstract

Under some pretty much weaker size conditions assumed on the integral kernels both on the unit sphere and in the radial directions, the Lp boundedness was given for the rough singular integrals defined by translates of a real-analytic submanifold in n. Certain Lp estimates for the corresponding maximal rough singular integrals were also established.

MSC 2010: 42B20; 42B15; 42B25

Communicated by Christopher D. Sogge


Award Identifier / Grant number: 11701333

Award Identifier / Grant number: 11771358

Award Identifier / Grant number: 11871101

Award Identifier / Grant number: 11471041

Award Identifier / Grant number: 11671039

Award Identifier / Grant number: 11761131002

Funding statement: The first author was partly supported by the NNSF of China (No. 11701333) and SP-OYSTTT-CMSS (No. Sxy2016K01). The second author was supported partly by NNSF of China (Nos. 11771358, 11871101). The third author was supported partly by NSFC (Nos. 11471041, 11671039, 11871101) and NSFC-DFG (No. 11761131002).

Acknowledgements

The authors want to express their sincere thanks to the referee for his or her valuable remarks and suggestions, which made this paper more readable.

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Received: 2019-05-13
Revised: 2019-09-22
Published Online: 2019-11-08
Published in Print: 2020-03-01

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