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A generalization of the Lions-Temam compact imbedding theorem. (English) Zbl 0755.46013
Summary: The well-known theorem by J. L. Lions and R. Temam concerning the compact imbedding of the space \(\{\nu\in L^ p(0,T;B_ 0)\); \(d\nu/dt\in L^ q(0,T;B_ 1)\}\) into \(L^ p(0,T;B)\) is generalized to the case when \(B_ 0\) is a reflexive Banach space imbedded compactly into a normed linear space \(B\) that is continuously imbedded into a Hausdorff locally convex space \(B_ 1\), and \(1<p<+\infty\), \(1\leq q\leq+\infty\). Applications of such generalization of numerical analysis are outlined.

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E40 Spaces of vector- and operator-valued functions
47B07 Linear operators defined by compactness properties