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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Singular integrals with rough kernels along real-analytic submanifolds in ${\mathbf{R}}^3$


Authors: Dashan Fan, Kanghui Guo and Yibiao Pan
Journal: Trans. Amer. Math. Soc. 355 (2003), 1145-1165
MSC (2000): Primary 42B20; Secondary 42B15, 42B25
Published electronically: November 5, 2002
MathSciNet review: 1938750
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Abstract: $L^p$ mapping properties will be established in this paper for singular Radon transforms with rough kernels defined by translates of a real-analytic submanifold in $\mathbf{R}^3$.


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Additional Information

Dashan Fan
Affiliation: Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201
Email: fan@csd4.csd.uwm.edu

Kanghui Guo
Affiliation: Department of Mathematics, Southwest Missouri State University, Springfield, Missouri 65804
Email: kag026f@smsu.edu

Yibiao Pan
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: yibiao+@pitt.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03175-6
PII: S 0002-9947(02)03175-6
Keywords: Singular integrals, oscillatory integrals, Fourier transform, maximal functions, $L^p$ boundedness, rough kernels, real-analytic submanifolds
Received by editor(s): March 16, 1998
Received by editor(s) in revised form: July 14, 2002
Published electronically: November 5, 2002
Additional Notes: This work was done during the second author’s visit at the Department of Mathematics, University of Pittsburgh
The third author was partially supported by NSF Grant DMS-9622979
Article copyright: © Copyright 2002 American Mathematical Society