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Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)
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Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Isroil A. Ikromov and Detlef Müller

Abstract

This is the first book to present a complete characterization of Stein–Tomas-type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all real-analytic hypersurfaces. The range of Lebesgue spaces for which these estimates are valid is described in terms of Newton polyhedra associated to the given surface. The book begins with Elias M. Stein's concept of Fourier restriction and some relations between the decay of the Fourier transform of the surface measure and Stein–Tomas-type restriction estimates. Varchenko's ideas relating Fourier decay to ... More

Keywords: Fourier restriction, smooth hypersurface, three dimensions, real-analytic hypersurface, Lebesgue spaces, Newton polyhedral, Fourier transform, Fourier decay, r-height

Bibliographic Information

Print publication date: 2016 Print ISBN-13: 9780691170541
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691170541.001.0001

Authors

Affiliations are at time of print publication.

Isroil A. Ikromov, author
Samarkind State University

Detlef Müller, author
Christian-Albrechts Universitat