Revista Matemática Iberoamericana

Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case

Shuanglin Shao

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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.

Article information

Rev. Mat. Iberoamericana, Volume 25, Number 3 (2009), 1127-1168.

First available in Project Euclid: 3 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B10: Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 42B25: Maximal functions, Littlewood-Paley theory
Secondary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

restriction conjecture Schrödinger equation cylindrical symmetry


Shao, Shuanglin. Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case. Rev. Mat. Iberoamericana 25 (2009), no. 3, 1127--1168.

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