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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rough singular integrals associated to surfaces of revolution


Authors: Shanzhen Lu, Yibiao Pan and Dachun Yang
Journal: Proc. Amer. Math. Soc. 129 (2001), 2931-2940
MSC (1991): Primary 42B20; Secondary 42B25, 47B38, 42B30, 43A90
Published electronically: February 15, 2001
MathSciNet review: 1840096
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Abstract:

Let $1<p<\infty$ and $n\ge 2$. The authors establish the $L^p(\mathbb{R}^{n+1})$-boundedness for a class of singular integral operators associated to surfaces of revolution, $\{(t,\phi(\vert t\vert)): t\in\mathbb{R}^n\}$, with rough kernels, provided that the corresponding maximal function along the plane curve $\{(t, \phi(\vert t\vert)): t\in\mathbb{R}\}$ is bounded on $L^p(\mathbb{R}^2)$.


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Additional Information

Shanzhen Lu
Affiliation: Department of Mathematics, Beijing Normal University, Beijing 100875, The People’s Republic of China
Email: lusz@bnu.edu.cn

Yibiao Pan
Affiliation: Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
Email: yibiao+@pitt.edu

Dachun Yang
Affiliation: Department of Mathematics, Beijing Normal University, Beijing 100875, The People’s Republic of China
Email: dcyang@bnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05893-2
PII: S 0002-9939(01)05893-2
Keywords: Curve, surface of revolution, singular integral, maximal operator, rough kernel, Hardy space, sphere
Received by editor(s): November 22, 1999
Received by editor(s) in revised form: February 10, 2000
Published electronically: February 15, 2001
Additional Notes: The first author was supported by the NNSF of China
The second author was supported by the NNSF of China
The third author was supported by the Croucher Foundation Chinese Visitorships 1999-2000 of Hong Kong and the NNSF of China
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2001 American Mathematical Society