Glasnik matematički, Vol. 53 No. 1, 2018.
Original scientific paper
https://doi.org/10.3336/gm.53.1.10
Proper inclusions of Morrey spaces
Hendra Gunawan
; Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia
Denny Ivanal Hakim
; Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia
Mochammad Idris
; Department of Mathematics, Bandung Institute of Technology, Bandung 40132, Indonesia
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].
Keywords
Morrey spaces; weak Morrey spaces; inclusion properties
Hrčak ID:
201828
URI
Publication date:
20.6.2018.
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