A note on the cone restriction conjecture in the cylindrically symmetric case
Abstract
In this note, 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 the 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 H\"older inequality in the Lorentz spaces.
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