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

By Shuanglin Shao. 2007

51 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e7722e785221e4e0af4ba7eb5f86dc2e469a0914

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Strichartz Estimates in Spherical Coordinates (2012, background): “As it was observed in [30, 25], the estimates have wider ranges of admissible p, q when φ is a radial function.”