Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T19:55:41.378Z Has data issue: false hasContentIssue false
  • English
  • Français

A Restriction Theorem for a k-Surface in ℝn

Published online by Cambridge University Press:  20 November 2018

Daniel M. Oberlin
Daniel M. Oberlin*
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, FL 32306-4510, U.S.A. e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We establish a sharp Fourier restriction estimate for a measure on a $k$-surface in ${{\mathbb{R}}^{n}}$, where $n\,=\,k\left( k\,+\,3 \right)/2$

Keywords

42B10Fourier restriction
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 2 , 01 June 2005 , pp. 260 - 266
Copyright
Copyright © Canadian Mathematical Society 2005

References

[BL] Bak, J.-G. and Lee, S., Restriction of the Fourier transform to a quadratic surface in ℝ n . Math. Z. 247(2004), 409–422.Google Scholar
[C1] Christ, M., Estimates for the k-plane transform. Indiana Univ. Math. J. 33(1984), 891–910.Google Scholar
[C2] Christ, M., On the restriction of the Fourier transform to curves: endpoint results and the degenerate case. Trans. Amer. Math. Soc. 287(1985), 223–238.Google Scholar
[CI] de Carli, L. and Iosevich, A., Some sharp restriction theorems for homogeneous manifolds. J. Fourier Analysis and Applications 4(1998), 105–128.Google Scholar
[CS] Carleson, L. and Sjölin, P., Oscillatory integrals and a multiplier problem for the disc. Studia Math. 44(1972), 287–299.Google Scholar
[F] Fefferman, C., Inequalities for strongly singular convolution operators. Acta Math. 124(1970), 9–36.Google Scholar
[M1] Mockenhaupt, G., Bounds in Lebesgue spaces of oscillatory integral operators. Habilitation thesis, Universität Siegen, 1996.Google Scholar
[M2] Mockenhaupt, G., Some remarks on oscillatory integrals. In: Geometric Analysis and Applications. Proc. CentreMath. Appl. Austral. Nat. Univ. 39, Canberra, 2001.Google Scholar
[M2] Prestini, E., Restriction theorems for the Fourier transform to some manifolds in ℝ n. In: Harmonic analysis in euclidean spaces. Proc. Sympos. Pure Math. 35, American Mathematics Society, Providence, RI, 1979, pp. 101–109.Google Scholar