Sobolev spaces on multiple cones

Abstract

The purpose of this note is to discuss how various Sobolev spaces defined on multiple cones behave with respect to density of smooth functions, interpolation and extension/restriction to/from \RR^n. The analysis interestingly combines use of Poincar\'e inequalities and of some Hardy type inequalities.Comment: Modifications following the referee's suggestions. Some typos and math typos corrected. Addition of references to Poincar\'e inequalities on sphere