On Burenkov's extension operator preserving Sobolev-Morrey spaces on Lipschitz domains

TL;DR

This paper proves that Burenkov's Extension Operator effectively preserves Sobolev spaces based on Morrey spaces on Lipschitz domains, including both bounded and unbounded sets, enhancing understanding of function extension in these spaces.

Contribution

It demonstrates that Burenkov's Extension Operator maintains Sobolev-Morrey space properties on Lipschitz domains, extending previous results to more general Morrey spaces and unbounded sets.

Findings

Burenkov's Extension Operator preserves Sobolev-Morrey spaces.

The results apply to both bounded and unbounded Lipschitz domains.

The analysis includes classical and general Morrey spaces.

Abstract

We prove that Burenkov's Extension Operator preserves Sobolev spaces built on general Morrey spaces, including classical Morrey spaces. The analysis concerns bounded and unbounded open sets with Lipschitz boundaries in the n-dimensional Euclidean space.