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

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

2007-06-26

arxiv.org/abs/0706.3759v3

Mathematics

Classical Analysis and ODEs

41 pages, 4 figures; referee's suggestions incorporated

Scientific paper

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 Schr\"odinger equation and establish the analogous results when the paraboloid is replaced by the lower third of the sphere.

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