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Criteria for monotonicity properties of Musielak-Orlicz spaces equipped with the Amemiya norm |
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| Authors: | Y. Cui L. Szymaszkiewicz |
| Affiliation: | a Department of Mathematics, Chongqing University of Post and Telecommunications, Harbin, PR China b Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland c Institute of Mathematics, Szczecin University, Wielkopolska 15, 70-451 Szczecin, Poland d Department of Mathematics, Harbin University of Sciences and Technology, Harbin, PR China |
| Abstract: | 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. |
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