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arXiv · 1702.07053

Proper inclusions of Morrey spaces

Hendra Gunawan·Denny I. Hakim·Mochammad Idris
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Abstract

In this paper, we prove that the inclusions between Morrey spaces, between weak Morrey spaces, and between a Morrey space and a weak Morrey space are all proper. The proper inclusion between a Morrey space and a weak Morrey space is established via the unboundedness of the Hardy-Littlewood maximal operator on Morrey spaces of exponent 1. In addition, we also give a necessary condition for each inclusion. Our results refine previous inclusion properties studied in [Gunawan et al, \emph{Math. Nachr.} {\bf 290} (2017), 332--340].

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Hendra Gunawan, Denny I. Hakim, Mochammad Idris. 2017-02-23. Proper inclusions of Morrey spaces. https://arxiv.org/abs/1702.07053

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