Morrey Sequence Spaces: Pitt's Theorem and compact embeddings

Dorothee D. Haroske; Leszek Skrzypczak

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arXiv · 1807.01184

Morrey Sequence Spaces: Pitt's Theorem and compact embeddings

Dorothee D. Haroske·Leszek Skrzypczak

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Abstract

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 $m_{u,p}=m_{u,p}(\mathbb{Z}^d)$, $0<p\leq u<\infty$, which have yet been considered almost nowhere. They are defined as natural generalizations of the classical $\ell_p$ spaces. We consider some basic features, embedding properties, the pre-dual, a corresponding version of Pitt's compactness theorem, and can further characterize the compactness of embeddings of related finite-dimensional spaces.

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BibTeX RIS

Dorothee D. Haroske, Leszek Skrzypczak. 2018-07-03. Morrey Sequence Spaces: Pitt's Theorem and compact embeddings. https://arxiv.org/abs/1807.01184

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