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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.

##### MSC:
 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