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Existence of extremals
for a Fourier restriction inequality
Michael Christ and Shuanglin Shao |
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Vol. 5 (2012), No. 2, 261–312
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Abstract |
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The adjoint Fourier restriction inequality of Tomas and Stein states that the mapping is bounded from to . 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
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Mathematical Subject Classification 2000
Primary: 42A38
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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
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Authors |
| Michael Christ | |
| University of California,
Berkeley Department of Mathematics Berkeley, CA 94720-3840 United States |
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| 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 |
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