Criteria for monotonicity properties of Musielak–Orlicz spaces equipped with the Amemiya norm

Criteria for strict monotonicity, lower local uniform monotonicity, upper local uniform monotonicity, and uniform monotonicity of Musielak–Orlicz spaces over any σ-finite and complete measure space, endowed with the Amemiya norm are given. The fact that the spaces are considered over arbitrary σ-fin...

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Bibliographic Details
Published in:	Journal of mathematical analysis and applications Vol. 303; no. 2; pp. 376 - 390
Main Authors:	Cui, Y., Hudzik, H., Szymaszkiewicz, L., Wang, T.
Format:	Journal Article
Language:	English
Published:	San Diego, CA Elsevier Inc 15-03-2005 Elsevier
Subjects:	Exact sciences and technology Functional analysis Mathematical analysis Mathematics Sciences and techniques of general use Lower bound Upper bound Orlicz space Mathematical analysis Amemiya norm Monotonicity
Online Access:	Get full text
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Summary:	Criteria for strict monotonicity, lower local uniform monotonicity, upper local uniform monotonicity, and uniform monotonicity of Musielak–Orlicz spaces over any σ-finite and complete measure space, endowed with the Amemiya norm are given. The fact that the spaces are considered over arbitrary σ-finite measure space is essential because, as it is shown in Example 3, the Musielak–Orlicz spaces need not be strictly monotone even if their restrictions to the nonatomic part and the purely atomic part are strictly monotone.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2004.07.026