An extension operator for Sobolev spaces with mixed weights

TL;DR

This paper develops an extension operator for weighted Sobolev spaces on polyhedral cones, accommodating mixed weights related to the cone's geometry, based on Stein's extension method.

Contribution

It introduces a new extension operator for Sobolev spaces with mixed weights on polyhedral cones, expanding the applicability of Stein's extension technique.

Findings

Extension operator for weighted Sobolev spaces on polyhedral cones.

Handles mixed weights related to cone geometry.

Based on Stein's extension operator.

Abstract

We provide an extension operator for weighted Sobolev spaces on bounded polyhedral cones $K$ involving a mixture of weights, which measure the distance to the vertex and the edges of the cone, respectively. Our results are based on Stein's extension operator for Sobolev spaces.