Vol. 5, No. 2, 2012

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Existence of extremals for a Fourier restriction inequality

Michael Christ and Shuanglin Shao

Vol. 5 (2012), No. 2, 261–312
Abstract

The adjoint Fourier restriction inequality of Tomas and Stein states that the mapping ffσ̂ is bounded from L2(S2) to L4(3). We prove that there exist functions that extremize this inequality, and that any extremizing sequence of nonnegative functions has a subsequence that converges to an extremizer.

Keywords
extremals, adjoint Fourier restriction inequality
Mathematical Subject Classification 2000
Primary: 42A38
Milestones
Received: 21 June 2010
Revised: 11 November 2010
Accepted: 22 December 2010
Published: 27 August 2012

Proposed: Terence Tao
Seconded: Steve Zelditch, Maciej Zworski
Authors
Michael Christ
University of California, Berkeley
Department of Mathematics
Berkeley, CA 94720-3840
United States
Shuanglin Shao
Institute for Mathematics and its Applications
University of Minnesota
Minneapolis, MN 55455
United States
School of Mathematics
Institute for Advanced Study
Princeton, NJ 08540
United States