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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Let and . The authors establish the -boundedness for a class of singular integral operators associated to surfaces of revolution, , with rough kernels, provided that the corresponding maximal function along the plane curve is bounded on .

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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

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