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

Shuanglin Shao

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

Classical Analysis and ODEs 2008-06-20 v2 Analysis of PDEs

Authors: Shuanglin Shao

Abstract

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.

Keywords

cone restriction conjecture cylindrically symmetric linear adjoint dyadic restriction estimate Hausdorff-Young inequality Hölder inequality Lorentz spaces

Cite

@article{arxiv.0710.1466,
  title  = {A note on the cone restriction conjecture in the cylindrically symmetric case},
  author = {Shuanglin Shao},
  journal= {arXiv preprint arXiv:0710.1466},
  year   = {2008}
}

Comments

9 pages, no figures. Referee's suggestions and comments incorporated; to appear the Proceedings of the AMS

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

Abstract

Keywords

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