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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Main Authors: HU Xuemei, CUI Yunan
Format: Article
Language:zho
Published: Harbin University of Science and Technology Publications 2024-04-01
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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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