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arXiv · 1508.00791

A Fourier Restriction Theorem For A Twodimensional Surface Of Finite Type

Stefan Buschenhenke·Detlef Müller·Ana Vargas
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Abstract

The problem of $L^p(R^3)\to L^2(S)$ Fourier restriction estimates for smooth hypersurfaces S of finite type in R^3 is by now very well understood for a large class of hypersurfaces, including all analytic ones. In this article, we take up the study of more general $L^p(R^3)\to L^q(S)$ Fourier restriction estimates, by studying a prototypical class of two-dimensional surfaces with strongly varying curvature conditions. Our approach is based on an adaptation of the so-called bilinear method. We discuss several new features arising in the study of this problem.

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Stefan Buschenhenke, Detlef Müller, Ana Vargas. 2015-11-13. A Fourier Restriction Theorem For A Twodimensional Surface Of Finite Type. https://doi.org/10.2140/apde.2017.10.817

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