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

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- by Shuanglin Shao
- Proc. Amer. Math. Soc.
**137**(2009), 135-143 - DOI: https://doi.org/10.1090/S0002-9939-08-09668-8
- Published electronically: August 26, 2008
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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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## Bibliographic 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