JournalsrmiVol. 25, No. 3pp. 1127–1168

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

  • Shuanglin Shao

    UCLA, Los Angeles, USA
Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case cover
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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.

Cite this article

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

DOI 10.4171/RMI/591