 
Summary: Compact Embeddings of VectorValued
Sobolev and Besov Spaces
Herbert Amann
In memoriam Branko Najman
1. Introduction and Main Results
Let E, E 0 , and E 1 be Banach spaces such that
E 1 ,\Gamma,! E ,! E 0 ; (1.1)
with ,! and ,\Gamma,! denoting continuous and compact embedding, respectively. Suppose
that p 0 ; p 1 2 [1; 1] and T ? 0, that
V is a bounded subset of L p1
\Gamma (0; T ); E 1
\Delta ; (1.2)
and that
@V := f @v ; v 2 V g is bounded in L p0
\Gamma
(0; T ); E 0
\Delta
; (1.3)
where @ denotes the distributional derivative. Then the wellknown `Aubin lemma',
more precisely, the `AubinDubinskii lemma' guarantees that
