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Morrey (function) spaces and, in particular, smoothness spaces of Besov-Morrey or Triebel-Lizorkin-Morrey type enjoyed a lot of interest recently. Here we turn our attention to Morrey sequence spaces mu,p =mu,p(Zd), 0<p\leq u<\infty, 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 can further characterize the compactness of embeddings of related finite-dimensional spaces. This is a joint work with Dorothee D. Haroske from F. Schiller University Jena (Germany).
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