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Gaussians rarely extremize adjoint Fourier restriction inequalities for paraboloids


Authors: Michael Christ and René Quilodrán
Journal: Proc. Amer. Math. Soc. 142 (2014), 887-896
MSC (2010): Primary 26D15, 35A15, 35B38, 42B10
DOI: https://doi.org/10.1090/S0002-9939-2013-11827-7
Published electronically: December 23, 2013
MathSciNet review: 3148523
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Abstract: It was proved independently by Foschi and by Hundertmark and Zharnitsky that Gaussians extremize the adjoint Fourier restriction inequality for $ L^2$ functions on the paraboloid in the two lowest-dimensional cases. Here we prove that Gaussians are critical points for the $ L^p$ to $ L^q$ adjoint Fourier restriction inequalities if and only if $ p=2$. Also, Gaussians are critial points for the $ L^2$ to $ L^r_t L^q_x$ Strichartz inequalities for all admissible pairs $ (r,q) \in (1,\infty )^2$.


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Additional Information

Michael Christ
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840
Email: mchrist@math.berkeley.edu

René Quilodrán
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720-3840
Email: rquilodr@math.berkeley.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11827-7
Received by editor(s): March 7, 2012
Published electronically: December 23, 2013
Additional Notes: The authors were supported in part by NSF grant DMS-0901569.
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2013 American Mathematical Society

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