Monotonicity in Modular Function Spaces Equipped with O-norm
Modular function spaces are extensions of Lebesgue spaces and Orlicz spaces. We introduce Orlicz norm in Modular function spaces, and study the monotonicity in modular function spaces equipped with O-norm and L-norm. Firstly, the paper demonstrates O-norm is equivalent to L-norm in modular functi...
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Harbin University of Science and Technology Publications
2024-04-01
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| Series: | Journal of Harbin University of Science and Technology |
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| Online Access: | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2324 |
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| _version_ | 1849320726579904512 |
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| author | HU Xuemei CUI Yunan |
| author_facet | HU Xuemei CUI Yunan |
| author_sort | HU Xuemei |
| collection | DOAJ |
| description |
Modular function spaces are extensions of Lebesgue spaces and Orlicz spaces. We introduce Orlicz norm in Modular function spaces, and study the monotonicity in modular function spaces equipped with O-norm and L-norm. Firstly, the paper demonstrates O-norm is equivalent to L-norm in modular function spaces, and modular function spaces equipped with O-norm are Banach spaces. Then, the paper demonstrates modular function spaces equipped with O-norm are strictly monotone. Lastly, the necessary and sufficient conditions of strict monotonicity of modular function spaces equipped with L-norm are given. |
| format | Article |
| id | doaj-art-4386ff3a975f4d9cb94afb987b53d5db |
| institution | Kabale University |
| issn | 1007-2683 |
| language | zho |
| publishDate | 2024-04-01 |
| publisher | Harbin University of Science and Technology Publications |
| record_format | Article |
| series | Journal of Harbin University of Science and Technology |
| spelling | doaj-art-4386ff3a975f4d9cb94afb987b53d5db2025-08-20T03:49:59ZzhoHarbin University of Science and Technology PublicationsJournal of Harbin University of Science and Technology1007-26832024-04-01290215315810.15938/j.jhust.2024.02.019Monotonicity in Modular Function Spaces Equipped with O-normHU Xuemei0CUI Yunan1School of Electric and Engineering, Harbin University of Science and Technology, Harbin 150080 ,ChinaSchool of Electric and Engineering, Harbin University of Science and Technology, Harbin 150080 ,China Modular function spaces are extensions of Lebesgue spaces and Orlicz spaces. We introduce Orlicz norm in Modular function spaces, and study the monotonicity in modular function spaces equipped with O-norm and L-norm. Firstly, the paper demonstrates O-norm is equivalent to L-norm in modular function spaces, and modular function spaces equipped with O-norm are Banach spaces. Then, the paper demonstrates modular function spaces equipped with O-norm are strictly monotone. Lastly, the necessary and sufficient conditions of strict monotonicity of modular function spaces equipped with L-norm are given.https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2324modular function spaceo-normstrict monotonicityl- norm |
| spellingShingle | HU Xuemei CUI Yunan Monotonicity in Modular Function Spaces Equipped with O-norm Journal of Harbin University of Science and Technology modular function space o-norm strict monotonicity l- norm |
| title | Monotonicity in Modular Function Spaces Equipped with O-norm |
| title_full | Monotonicity in Modular Function Spaces Equipped with O-norm |
| title_fullStr | Monotonicity in Modular Function Spaces Equipped with O-norm |
| title_full_unstemmed | Monotonicity in Modular Function Spaces Equipped with O-norm |
| title_short | Monotonicity in Modular Function Spaces Equipped with O-norm |
| title_sort | monotonicity in modular function spaces equipped with o norm |
| topic | modular function space o-norm strict monotonicity l- norm |
| url | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2324 |
| work_keys_str_mv | AT huxuemei monotonicityinmodularfunctionspacesequippedwithonorm AT cuiyunan monotonicityinmodularfunctionspacesequippedwithonorm |