Revista Matemática Iberoamericana


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Volume 25, Issue 3, 2009, pp. 1127–1168
DOI: 10.4171/RMI/591

Published online: 2009-12-31

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

Shuanglin Shao[1]

(1) UCLA, Los Angeles, USA

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.

Keywords: Restriction conjecture, Schrödinger equation, cylindrical symmetry

Shao Shuanglin: Sharp linear and bilinear restriction estimates for paraboloids in the cylindrically symmetric case. Rev. Mat. Iberoam. 25 (2009), 1127-1168. doi: 10.4171/RMI/591