# On Stein's extension operator preserving Sobolev-Morrey spaces

## TL;DR

This paper proves that Stein's Extension Operator maintains the structure of Sobolev-Morrey spaces, which are function spaces characterized by weak derivatives in Morrey spaces, on various domains.

## Contribution

The paper establishes the preservation property of Stein's Extension Operator for Sobolev-Morrey spaces on Lipschitz domains, extending previous results to more general settings.

## Key findings

- Stein's Extension Operator preserves Sobolev-Morrey spaces.
- The results apply to classical and generalized Morrey spaces.
- The analysis covers bounded and unbounded Lipschitz domains.

## Abstract

We prove that Stein's Extension Operator preserves Sobolev-Morrey spaces, that is spaces of functions with weak derivatives in Morrey spaces. The analysis concerns classical and generalized Morrey spaces on bounded and unbounded domains with Lipschitz boundaries in the n-dimensional Euclidean space.