Weighted fractional Sobolev spaces as interpolation spaces in bounded domains

TL;DR

This paper characterizes the interpolation space between weighted L^p and Sobolev spaces in bounded domains, using weights based on the distance to the boundary, advancing understanding of fractional Sobolev spaces.

Contribution

It provides a new characterization of real interpolation spaces involving weighted Sobolev spaces with boundary-distance weights in arbitrary bounded domains.

Findings

Identifies the interpolation space as a weighted fractional Sobolev space.

Extends previous results to arbitrary bounded domains with boundary weights.

Clarifies the structure of weighted fractional Sobolev spaces in interpolation theory.

Abstract

We characterize the real interpolation space between a weighted $L^p$ space and a weighted Sobolev space in arbitrary bounded domains in $\mathbb{R}^n$, with weights that are positive powers of the distance to the boundary.