Sobolev trace inequality on $W^{s,q}(\mathbb{R}^n)$

TL;DR

This paper establishes Sobolev trace inequalities within nonhomogeneous fractional Sobolev spaces, expanding the mathematical understanding of boundary behavior in these function spaces.

Contribution

The paper introduces new Sobolev trace inequalities specifically for nonhomogeneous fractional Sobolev spaces, which were not previously well-understood.

Findings

Established Sobolev trace inequalities for nonhomogeneous fractional Sobolev spaces

Extended classical trace inequalities to fractional and nonhomogeneous settings

Provided new tools for analysis in fractional Sobolev spaces

Abstract

Sobolev trace inequalities on nonhomogeneous fractional Sobolev spaces are established.