Generalised Morrey sequence spaces

TL;DR

This paper introduces generalized Morrey sequence spaces, extending classical Morrey sequence spaces, and investigates their fundamental properties and embedding relations relevant to analysis and PDE applications.

Contribution

It defines and studies the basic features and embedding properties of generalized Morrey sequence spaces, extending classical concepts to a more general setting.

Findings

Spaces include classical Morrey sequence spaces as special cases

Established embedding, continuity, and compactness properties

Analyzed strict singularity of embeddings

Abstract

Generalised Morrey (function) spaces enjoyed some interest recently and found applications to PDE. Here we turn our attention to their discrete counterparts. We define generalised Morrey sequence spaces $m_{\varphi,p}=m_{\varphi,p}(\mathbb{Z}^d)$. They are natural generalisations of the classical Morrey sequence spaces $m_{u,p}$, $0<p\le u<\infty$, which were studied earlier. We consider some basic features of the spaces as well as embedding properties such as continuity, compactness and strict singularity.