Glasnik Matematicki, Vol. 53, No. 1 (2018), 143-151.

PROPER INCLUSIONS OF MORREY SPACES

Hendra Gunawan, Denny Ivanal Hakim and Mochammad Idris

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 [4].

2010 Mathematics Subject Classification.   42B35, 46E30.

Key words and phrases.   Morrey spaces, weak Morrey spaces, inclusion properties.

DOI: 10.3336/gm.53.1.10

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