Following Yu. A. Dubinskij, the author considers the Sobolev space of infinite order \[ W^{\infty}\{a_ n,p,r\}_ G=\{u(x)\in C^{\infty}(G);\quad \sum^{\infty}_{n=0}a_ n\| L^ nu\|^ p_{L_ r(G)}<\infty \}. \] She establishes sufficient conditions for the embedding \[ W^{\infty}\{a_ n,p,r\}_ G\subset W^{\infty}\{b_ n,p,r\}_ G \] in the case of G equal to the real axis, or the positive halfaxis, or a segment, or a circumference. Besides it, the author improves the Kolmogorov-Stein inequality for infinitely differentiable functions, and writes down a generalization of the Mandelbrojt theorem about imbedding of classes \(C_ R(L_ n)\). \((F\in C_ R(L_ n)\) iff there exists \(t=t(F)\) such that \(\| D^ nF\|_ C\leq t^ nL_ n.)\)