A note on the cone restriction conjecture in the cylindrically symmetric case

Shao, Shuanglin

doi:10.1090/S0002-9939-08-09668-8

A note on the cone restriction conjecture in the cylindrically symmetric case
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Proc. Amer. Math. Soc. 137 (2009), 135-143 Request permission

Abstract:

In this paper, we present two arguments showing that the classical linear adjoint cone restriction conjecture holds for the class of functions supported on the cone and invariant under spatial rotation in all dimensions. The first is based on a dyadic restriction estimate, while the second follows from a strengthening version of the Hausdorff-Young inequality and the Hölder inequality in Lorentz spaces.

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