Tohoku Mathematical Journal

On singular integrals associated to surfaces

Feng Liu

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Abstract

This paper is devoted to studying the singular integral with rough kernel associated to surfaces, which contain many classical surfaces as model examples. Also, the kernel of our operator lacks smoothness on the unit sphere as well as in the radial direction. We obtain the $L^p$ boundedness of the singular integral under a sharp size condition on its kernels in an extrapolation argument. In addition, the corresponding results for maximal truncated singular integral operators are also established.

Article information

Source
Tohoku Math. J. (2), Volume 66, Number 1 (2014), 1-14.

Dates
First available in Project Euclid: 7 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1396875659

Digital Object Identifier
doi:10.2748/tmj/1396875659

Mathematical Reviews number (MathSciNet)
MR3189476

Zentralblatt MATH identifier
1293.42015

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 42B99: None of the above, but in this section

Keywords
Singular integral rough kernel extrapolation

Citation

Liu, Feng. On singular integrals associated to surfaces. Tohoku Math. J. (2) 66 (2014), no. 1, 1--14. doi:10.2748/tmj/1396875659. https://projecteuclid.org/euclid.tmj/1396875659


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