Embedding of vector-valued Morrey spaces and separable differential operators

The paper is the first part of a program devoted to the study of the behavior of operator-valued multipliers in Morrey spaces. Embedding theorems and uniform separability properties involving E-valued Morrey spaces are proved. As a consequence, maximal regularity for solutions of infinite systems of anisitropic elliptic partial differential equations are established. © 2018, The Author(s).