Functional characterizations of trace spaces in Lipschitz domains

Abstract

Using a factorization theorem of Douglas, we prove functional characterizations of trace spaces $H^s(\partial \Omega )$ involving a family of positive self-adjoint operators. Our method is based on the use of a suitable operator by taking the trace on the boundary $\partial \Omega$ of a bounded Lipschitz domain $\Omega \subset {\mathbb{R}}^d$ and applying Moore–Penrose pseudoinverse properties together with a special inner product on $H^1(\Omega )$. We also establish generalized results of the Moore–Penrose pseudoinverse.