Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



$L^p$ regularity of averaging operators with higher fold singularities

Author: Chan Woo Yang
Journal: Proc. Amer. Math. Soc. 131 (2003), 455-465
MSC (2000): Primary 44A12; Secondary 35S30
Published electronically: June 5, 2002
MathSciNet review: 1933337
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we give a sharp $L^p$ regularity result of averaging operators along curves in the plane with two-sided $k-$fold singularities.

References [Enhancements On Off] (What's this?)

  • [Ch] M. Christ, Failure of an endpoint estimate for integral along curves, Fourier analysis and partial differential equations, ed. by J. Garcia-Cuerva, E. Hernandez, F. Soria and J.L. Torrea, CRC Press, 1995. MR 97e:44007
  • [C] S. Cuccagna, $L^2$ estimates for averaging operators along curves with two-sided k-fold singularities, Duke Math. Journal, 89(2) (1997), 203-216. MR 99f:58199
  • [G] M. Greenblatt, A method for proving $L^p$ boundedness of singular Radon transforms in codimension one for $1<p<\infty$, Duke Math. Journal, 108(2) (2001), 363-393.
  • [I] A. Iosevich, Maximal operators associated to families of flat curves in the plane, Duke Math. Journal, 76(2) (1994), 633-644. MR 95k:42028
  • [PSt1] D. H. Phong and E. M. Stein, Models of degenerate Fourier integral operators and Radon transforms, Ann. Math., 140(1994), 703-722. MR 96c:35206
  • [PSt2] D. H. Phong and E. M. Stein, Radon transforms and torsion, Internat. Math. Res. Notices, 1991, 49-60. MR 96c:35206
  • [S1] A. Seeger, Degenerate Fourier integral operators in the plane, Duke Math. J., 71 (1993), 685-745. MR 94h:35292
  • [S2] A. Seeger, Radon transforms and finite type conditons, J. Amer. Math. Soc., 11 (1998), 869-897. MR 99f:58202

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 44A12, 35S30

Retrieve articles in all journals with MSC (2000): 44A12, 35S30

Additional Information

Chan Woo Yang
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

Keywords: Radon transform, $k-$fold singularity, nonisotropic ball
Received by editor(s): May 21, 2001
Received by editor(s) in revised form: September 11, 2001
Published electronically: June 5, 2002
Communicated by: Andreas Seeger
Article copyright: © Copyright 2002 American Mathematical Society