Universal extension for Sobolev spaces of differential forms and applications (Q442182)

Let \(\Omega\) be a bounded Lipschitz domain in a Euclidean space \(\mathbb R^ d\). The authors construct a family of universal extension operators for a Sobolev space containing differential forms of degree not exceeding \(d\) from \(\Omega\) to the entire space \(\mathbb R^ d\). It is emphasized that the extension operators are universal, generalizing thereby the classical result of \textit{E. M. Stein} ([Singular integrals and differentiability properties of functions. Princeton University Press (1970; Zbl 0207.13501)], Theorem~5, p.\,181). The results are presented only in the case when the Sobolev space is a Hilbert space.