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

 

Adjoint restriction estimates and scaling on spheres


Author: Bassam Shayya
Journal: Proc. Amer. Math. Soc. 132 (2004), 1517-1524
MSC (2000): Primary 42B10, 42B15
Published electronically: October 3, 2003
MathSciNet review: 2053360
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Abstract: We test the restriction conjecture, in its adjoint form, against a class of measures $\phi_\delta d\sigma$ on the sphere ${\bf S}^{n-1}$. The densities $\phi_\delta$ are smoothed out characteristic functions of $\delta^{a_2} \times \delta^{a_3} \times \dots \times \delta^{a_n}$ rectangular caps on ${\bf S}^{n-1}$, where $a_2, a_3, \dots, a_n$are fixed nonnegative numbers.


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Additional Information

Bassam Shayya
Affiliation: Department of Mathematics, American University of Beirut, Beirut, Lebanon
Email: bshayya@aub.edu.lb

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07258-7
PII: S 0002-9939(03)07258-7
Received by editor(s): May 20, 2002
Received by editor(s) in revised form: January 28, 2003
Published electronically: October 3, 2003
Communicated by: Andreas Seeger
Article copyright: © Copyright 2003 American Mathematical Society