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

In this note, we present two arguments showing that the classical \textit{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.Comment: 9 pages, no figures. Referee's suggestions and comments incorporated; to appear the Proceedings of the AM