Functional characterizations of trace spaces in Lipschitz domains

Abstract

Using a factorization theorem of Douglas, we prove functional characterizations of trace spaces H s (∂Ω) involving a family of positive selfadjoint operators. Our method is based on the use of a suitable operator by taking the trace on the boundary ∂Ω of a bounded Lipschitz domain Ω ⊂ R d and applying Moore-Penrose pseudo-inverse properties together with a special inner product on H 1 (Ω). Moreover, generalized results of the Moore-Penrose pseudo-inverse are also established. * Corresponding author. 2010 Mathematics Subject Classification. Primary 46E35; Secondary 47A05, 15A09.