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

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  01 August 2008

JONG-GUK BAK ,
DANIEL M. OBERLIN  and
ANDREAS SEEGER
JONG-GUK BAK
Affiliation:
Department of Mathematics and the Pohang Mathematics Institute, Pohang University of Science and Technology, Pohang 790-784, Korea (email: [email protected])
DANIEL M. OBERLIN
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA (email: [email protected])
ANDREAS SEEGER*
Affiliation:
Department of Mathematics, University of Wisconsin–Madison, Madison, WI 53706, USA (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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Weconsider the Fourier restriction operators associated to certaindegenerate curves in ℝd 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.

Keywords

restriction of Fourier transformsFourier extension operatoraffine arclength measure

MSC classification

Secondary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 42B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 1 , August 2008 , pp. 1 - 28
Copyright
Copyright © 2008 Australian Mathematical Society

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.

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