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

 

Remarks on the degenerate Radon transform in $\mathbf{R}^{2}$


Author: Sang Hyuk Lee
Journal: Proc. Amer. Math. Soc. 129 (2001), 3373-3378
MSC (2000): Primary 44A12; Secondary 47G10
Published electronically: April 25, 2001
MathSciNet review: 1845015
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Abstract: The aim of this note is to prove endpoint boundedness of the generalized Radon transform which was introduced by Phong and Stein. M. Christ's combinatorial method is used to obtain restricted weak type at the endpoints. Also we show that the results of this note are essentially optimal.


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Additional Information

Sang Hyuk Lee
Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang 790-784, Korea
Email: huk@euclid.postech.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05956-1
PII: S 0002-9939(01)05956-1
Keywords: Radon transform, degenerate
Received by editor(s): July 2, 1999
Received by editor(s) in revised form: April 3, 2000
Published electronically: April 25, 2001
Additional Notes: The author was supported in part by KOSEF grant no. 1999-2-102-003-5 and BK21 Project.
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2001 American Mathematical Society