``Traces'' of functions from Sobolev-Orlicz classes of infinite order (Q1083660)

This paper deals with the theory of traces of members of Sobolev-Orlicz classes of infinite order. A family \(\{f_{\omega}:\omega =(\omega_ 1,...,\omega_ n)\) a multi-index\(\}\) of functions \(f_{\omega}\) defined on the boundary \(\partial \Omega\) of a domain \(\Omega\) in \({\mathbb{R}}^ n\) is called the trace of a function u on \({\bar \Omega}\) if \(D^{\omega}u=f_{\omega}\) on \(\partial \Omega\) for all \(\omega\). for certain admissible domains \(\Omega\), necessary and sufficient conditions are obtained for a family \(\{f_{\omega}\}\) to be the trace of a function u in a Sobolev-Orlicz class of infinite order. More readily verifiable sufficient conditions are also obtained in the case \(n=1\).