$L^p-L^2$ Fourier restriction for hypersurfaces in $\Bbb R^3$: Part I

Isroil A. Ikomov; Detlef Müller

$L^p-L^2$ Fourier restriction for hypersurfaces in $\Bbb R^3$: Part I

Classical Analysis and ODEs 2014-10-14 v2 Analysis of PDEs

Authors: Isroil A. Ikomov , Detlef Müller

Abstract

This is the first of two articles in which we prove a sharp $L^p-L^2$ Fourier restriction theorem for a large class of smooth, finite type hypersurfaces in $\Bbb R^3$ , which includes in particular all real-analytic hypersurfaces. The present file is a modified and extended version of an earlier file of the same title. Some changes and corrections had become necessary, in order to make sure that Part II is really compatible with Part I, and it is recommended to replace the earlier version of Part I by the new one.

Keywords

fourier restriction hypersurfaces lp-l2 estimates finite type real-analytic harmonic analysis sharp theorem

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@article{arxiv.1208.6090,
  title  = {$L^p-L^2$ Fourier restriction for hypersurfaces in $\Bbb R^3$: Part I},
  author = {Isroil A. Ikomov and Detlef Müller},
  journal= {arXiv preprint arXiv:1208.6090},
  year   = {2014}
}

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99 pages, 2 figures

$L^p-L^2$ Fourier restriction for hypersurfaces in $\Bbb R^3$: Part I

Abstract

Keywords

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