On conditions for extending the trace and imbedding for Banach spaces of infinitely differentiable functions

This paper is a continuation of investigations begun in [1]–[3]. Conditions are obtained for the existence of a function in an infinite-order Sobolev space with specified values of the function itself and of all its derivatives on the boundary of the domain, and criteria are established for imbeddings and compact imbeddings of some of the indicated spaces.