Proper inclusions of Morrey spaces
Functional Analysis
2018-02-20 v2
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].
Keywords
Cite
@article{arxiv.1702.07053,
title = {Proper inclusions of Morrey spaces},
author = {Hendra Gunawan and Denny I. Hakim and Mochammad Idris},
journal= {arXiv preprint arXiv:1702.07053},
year = {2018}
}
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8 pages