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 pseudo-inverse properties together with a special inner product on $H^1(\Omega )$. Moreover, generalized results of the Moore--Penrose pseudo-inverse are also established.

This is a preprint of a paper whose final and definite form is with 'Banach J. Math. Anal.', ISSN: 1735-8787, available at [https://projecteuclid.org/info/euclid.bjma]. Submitted 21-Aug-2018; Article accepted on 30-Nov-2018