Affine Poisson & Non-Poisson trace principles for $\dot{H}^{-1<-\alpha\le-\frac12}(\R^{n-1})$

TL;DR

This paper introduces new trace inequalities for Sobolev functions involving fractional derivatives, expanding the understanding of affine and non-Poisson trace principles with sharp and non-sharp versions.

Contribution

It establishes both affine non-sharp-Poisson and sharp non-Poisson trace inequalities for fractional Sobolev functions, advancing the theoretical framework.

Findings

Derived affine non-sharp-Poisson trace inequality

Established sharp non-Poisson trace inequality

Extended trace principles to fractional Sobolev spaces

Abstract

This note discovers not only an affine non-sharp-Poisson trace inequality but also its sharp-non-Poisson version for a Sobolev function with the fractional antiderivative.