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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on the cone restriction conjecture in the cylindrically symmetric case


Author: Shuanglin Shao
Journal: Proc. Amer. Math. Soc. 137 (2009), 135-143
MSC (2000): Primary 42B10, 42B25; Secondary 35L05
Published electronically: August 26, 2008
MathSciNet review: 2439434
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Abstract: In this paper, we present two arguments showing that the classical linear adjoint cone restriction conjecture holds for the class of functions supported on the cone and invariant under spatial rotation in all dimensions. The first is based on a dyadic restriction estimate, while the second follows from a strengthening version of the Hausdorff-Young inequality and the Hölder inequality in Lorentz spaces.


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Additional Information

Shuanglin Shao
Affiliation: Department of Mathematics, University of California, Los Angeles, California 90095-1555
Address at time of publication: School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540
Email: slshao@math.ucla.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09668-8
PII: S 0002-9939(08)09668-8
Received by editor(s): October 9, 2007
Published electronically: August 26, 2008
Communicated by: Hart F. Smith
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.