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

PROPER INCLUSIONS OF MORREY SPACES

Hendra Gunawan, Denny Ivanal Hakim and Mochammad Idris

Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia
e-mail: hgunawan@math.itb.ac.id
e-mail: dennyivanalhakim@gmail.com
e-mail: idemath@gmail.com

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.


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DOI: 10.3336/gm.53.1.10


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