Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 66, Number 1 (2014), 1-14.
On singular integrals associated to surfaces
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.
Tohoku Math. J. (2), Volume 66, Number 1 (2014), 1-14.
First available in Project Euclid: 7 April 2014
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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