A note on the cone restriction conjecture in the cylindrically symmetric case
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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.References
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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
- Received by editor(s): October 9, 2007
- Published electronically: August 26, 2008
- Communicated by: Hart F. Smith
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 135-143
- MSC (2000): Primary 42B10, 42B25; Secondary 35L05
- DOI: https://doi.org/10.1090/S0002-9939-08-09668-8
- MathSciNet review: 2439434