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$L^p$ improving estimates for some classes of Radon transforms


Author: Chan Woo Yang
Journal: Trans. Amer. Math. Soc. 357 (2005), 3887-3903
MSC (2000): Primary 44A12; Secondary 35S30
DOI: https://doi.org/10.1090/S0002-9947-05-03807-9
Published electronically: May 4, 2005
MathSciNet review: 2159692
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Abstract: In this paper, we give $L^p-L^q$ estimates and the $L^p$ regularizing estimate of Radon transforms associated to real analytic functions, and we also give estimates of the decay rate of the $L^p$ operator norm of corresponding oscillatory integral operators. For $L^p-L^q$estimates and estimates of the decay rate of the $L^p$ operator norm we obtain sharp results except for extreme points; however, for $L^p$regularity we allow some restrictions on the phase function.


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Additional Information

Chan Woo Yang
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Address at time of publication: Department of Mathematics, Korea University, 1 Anam-dong, Sungbuk-ku, Seoul, Korea 136-701

DOI: https://doi.org/10.1090/S0002-9947-05-03807-9
Keywords: Oscillatory integral operator, Radon transform
Received by editor(s): September 11, 2001
Received by editor(s) in revised form: October 29, 2002
Published electronically: May 4, 2005
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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