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Tohoku Mathematical Journal
SECOND SERIES VOL. 66, NO. 1
|Tohoku Math. J.|
66 (2014), 1-14
ON SINGULAR INTEGRALS ASSOCIATED TO SURFACES
(Received November 20, 2012, revised April 5, 2013)
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.
Mathematics Subject Classification.
Primary 42B20; Secondary 42B25, 42B99.
Key words and phrases.
Singular integral, rough kernel, extrapolation.
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