improving estimates for some classes of Radon transforms
Author:
Chan Woo Yang
Journal:
Trans. Amer. Math. Soc. 357 (2005), 38873903
MSC (2000):
Primary 44A12; Secondary 35S30
Published electronically:
May 4, 2005
MathSciNet review:
2159692
Fulltext PDF Free Access
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Abstract: In this paper, we give estimates and the regularizing estimate of Radon transforms associated to real analytic functions, and we also give estimates of the decay rate of the operator norm of corresponding oscillatory integral operators. For estimates and estimates of the decay rate of the operator norm we obtain sharp results except for extreme points; however, for regularity we allow some restrictions on the phase function.
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 JG. Bak, An estimate for Radon transforms associated to polynomials, Duke Math. Journal, 101 (2000), 259269. MR 1738178 (2001b:42012)
 [BOS]
 JG. Bak, D. Oberlin and A. Seeger Two endpoint bounds for generalized Radon transforms in the plane, Rev. Mat. Iberoamericana, 18 (2002), 231247. MR 1924693 (2003h:44002)
 [Ch1]
 M. Christ, Hilbert transforms along curves, I. Nilpotent groups, Ann. Math., 122 (1985), 575596. MR 0819558 (87f:42039a)
 [Ch2]
 M. Christ, Failure of an endpoint estimate for integral along curves, Fourier analysis and partial differential equations, ed. by J. GarciaCuerva, E. Hernandez, F. Soria and J.L. Torrea, CRC Press, 1995. MR 1330238 (97e:44007)
 [CSWW]
 A. Carbery, A. Seeger, S. Wainger and J. Wright, Classes of singular integral operators along variable lines, J. Geom. Anal., 9 (1999), 583609. MR 1757580 (2001g:42026)
 [GS]
 A. Greenleaf and A. Seeger, On oscillatory integral operators with folding canonical relations, Studia Math., 132(2)(1999), 125139. MR 1669698 (2000g:58040)
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 S. Lee, Endpoint estimates for degenerate Radon transforms in associated with real analytic functions, Corrected reprint of Math. Z., 243 (2003), no. 2, 217241 [MR 1961865 (2004g:47065a)]. Math. Z., 243 (2003), no. 4, 817841. MR 1974584 (2004g:47065b)
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 D. H. Phong and E. M. Stein, Damped oscillatory integral operators with analytic phases, Adv. in Math., 134 (1998), 146177. MR 1612395 (2000b:42009)
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 D. H. Phong and E. M. Stein, The Newton polyhedron and oscillatory integral operators, Acta Math., 179 (1997), 105152. MR 1484770 (98j:42009)
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 D. H. Phong and E. M. Stein, Models of degenerate Fourier integral operators and Radon transforms, Ann. Math., 140 (1994), 703722. MR 1307901 (96c:35206)
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 V. S. Rychkov, Sharp bounds for oscillatory integral operators with phases, Math. Z., 236 (2001), 461489. MR 1821301 (2002i:42016)
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 A. Seeger, Degenerate Fourier integral operators in the plane, Duke Math. J., 71 (1993), 685745. MR 1240601 (94h:35292)
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 A. Seeger, Radon transforms and finite type conditons, J. Amer. Math. Soc., 11 (1998), 869897. MR 1623430 (99f:58202)
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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 Anamdong, Sungbukku, Seoul, Korea 136701
DOI:
http://dx.doi.org/10.1090/S0002994705038079
PII:
S 00029947(05)038079
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.
