Proper inclusions of Morrey spaces

2017/02/23 by Gunawan, Hendra, Hakim, Denny I., Idris, Mochammad · 1 citation
#42B35 #46E30 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1702.07053

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, Math. Nachr. \bf 290 (2017), 332--340].

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