Journal of the Australian Mathematical Society

Research Article

RESTRICTION OF FOURIER TRANSFORMS TO CURVES II: SOME CLASSES WITH VANISHING TORSION

JONG-GUK BAKa1, DANIEL M. OBERLINa2 and ANDREAS SEEGERa3 c1

a1 Department of Mathematics and the Pohang Mathematics Institute, Pohang University of Science and Technology, Pohang 790-784, Korea (email: bak@postech.ac.kr)

a2 Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA (email: oberlin@math.fsu.edu)

a3 Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706, USA (email: seeger@math.wisc.edu)

Abstract

We consider the Fourier restriction operators associated to certain degenerate curves in xs211Dd for which the highest torsion vanishes. We prove estimates with respect to affine arclength and with respect to the Euclidean arclength measure on the curve. The estimates have certain uniform features, and the affine arclength results cover families of flat curves.

(Received January 17 2007)

(Accepted June 04 2007)

2000 Mathematics subject classification

  • 42B10;
  • 42B99

Keywords and phrases

  • restriction of Fourier transforms;
  • Fourier extension operator;
  • affine arclength measure

Correspondence:

c1 For correspondence; e-mail: seeger@math.wisc.edu

Footnotes

J.B. was supported in part by grant R01-2004-000-10055-0 of the Korea Science and Engineering Foundation. D.O. was supported in part by NSF grant DMS-0552041. A.S. was supported in part by NSF grant DMS-0200186.