EMBEDDING THEOREMS IN BANACH -VALUED SOBOLEV-LIOUVILLE SPACES AND THEIR APPLICATIONS

In this paper we introduce a Banach- valued Sobolev-Liouville spaces associated with Banach spaces E1,E and some parameters and proved continuity and compacness of embedding operators in these spaces in terms of theory interpolations of Banach spaces uniformly with respect to these parameters and proved estimate of semigroup operator in weighted spaces. This problem arises in the investigation of boundary value problems for differential-operator equations with parameters.Further we consider certain class of partial differential -operator equation with parameters in Lp spaces and establish coercive solvability of this problem uniformly with respect to these parameters.