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Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case
Shuanglin
Shao
Source: Rev. Mat. Iberoamericana Volume 25, Number 3
(2009), 1127-1168.
Abstract
For cylindrically symmetric functions dyadically supported on the paraboloid, we obtain a family of sharp linear and bilinear adjoint restriction estimates. As corollaries, we first extend the ranges of exponents for the classical \textit{linear or bilinear adjoint restriction conjectures} for such functions and verify the \textit{linear adjoint restriction conjecture} for the paraboloid. We also interpret the restriction estimates in terms of solutions to the Schrödinger equation and establish the analogous results when the paraboloid is replaced by the lower third of the sphere.
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Permanent link to this document: http://projecteuclid.org/euclid.rmi/1257258103
Zentralblatt MATH identifier: 05663372
Mathematical Reviews number (MathSciNet): MR2590695
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