Morrey Sequence Spaces: Pitt's Theorem and Compact Embeddings

Morrey (function) spaces and, in particular, smoothness spaces of Besov-Morrey or Triebel-Lizorkin-Morrey type have enjoyed a lot of interest recently. Here we turn our attention to Morrey sequence spaces mu,p=mu,p(Zd), 0<p <= u<infinity, which have yet been considered almost nowhere. They are defined as natural generalizations of the classical lp spaces. We consider some basic features, embedding properties, a pre-dual, a corresponding version of Pitt's compactness theorem, and further characterize the compactness of embeddings of related finite-dimensional spaces.