Abstract-valued Orlicz spaces of range-varying type
This paper mainly deals with the abstract-valued Orlicz spaces of range-varying type. Using notions of Banach space net and continuous modular net etc., we give definitions of Lϱθ(⋅)(I, Xθ(⋅)) and L+ϱθ(⋅)$\begin{array}{} L_{+}^{\varrho_{\theta(\cdot)}} \end{array} $(I, Xθ(⋅)), and discuss their geo...
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doaj-c3fb6aa1207f4241854444269f359ae92021-09-06T19:20:10ZengDe GruyterOpen Mathematics2391-54552018-08-0116192495410.1515/math-2018-0080math-2018-0080Abstract-valued Orlicz spaces of range-varying typeZhang Qinghua0Department of Mathematics, Nantong University, 9 Seyuan Road, Nantong City, 226019, Jiangsu Province, ChinaThis paper mainly deals with the abstract-valued Orlicz spaces of range-varying type. Using notions of Banach space net and continuous modular net etc., we give definitions of Lϱθ(⋅)(I, Xθ(⋅)) and L+ϱθ(⋅)$\begin{array}{} L_{+}^{\varrho_{\theta(\cdot)}} \end{array} $(I, Xθ(⋅)), and discuss their geometrical properties as well as the representation of L+ϱθ(⋅)$\begin{array}{} L_{+}^{\varrho_{\theta(\cdot)}} \end{array} $(I, Xθ(⋅))*. We also investigate some functionals and operators on Lϱθ(⋅)(I, Xθ(⋅)), giving expression for the subdifferential of the convex functional generated by another continuous modular net. After making some investigations on the Bochner-Sobolev spaces W1, ϱθ(⋅)(I, Xθ(⋅)) and Wper1,ϱθ(⋅)$\begin{array}{} W_{\textrm{per}}^{1,\varrho_{\theta(\cdot)}} \end{array} $(I, Xθ(⋅)), and the intersection space Wper1,ϱθ(⋅)$\begin{array}{} W_{\textrm{per}}^{1,\varrho_{\theta(\cdot)}} \end{array} $(I, Xθ(⋅)) ∩ Lφϑ(⋅)(I, Vϑ(⋅)), a second order differential inclusion together with an anisotropic nonlinear elliptic equation with nonstandard growth are also taken into account.https://doi.org/10.1515/math-2018-0080continuous modular netxθ(⋅)–valued function spacegeometrical propertydoubly nonlinear differential inclusion46b1046e3046e40 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Zhang Qinghua |
spellingShingle |
Zhang Qinghua Abstract-valued Orlicz spaces of range-varying type Open Mathematics continuous modular net xθ(⋅)–valued function space geometrical property doubly nonlinear differential inclusion 46b10 46e30 46e40 |
author_facet |
Zhang Qinghua |
author_sort |
Zhang Qinghua |
title |
Abstract-valued Orlicz spaces of range-varying type |
title_short |
Abstract-valued Orlicz spaces of range-varying type |
title_full |
Abstract-valued Orlicz spaces of range-varying type |
title_fullStr |
Abstract-valued Orlicz spaces of range-varying type |
title_full_unstemmed |
Abstract-valued Orlicz spaces of range-varying type |
title_sort |
abstract-valued orlicz spaces of range-varying type |
publisher |
De Gruyter |
series |
Open Mathematics |
issn |
2391-5455 |
publishDate |
2018-08-01 |
description |
This paper mainly deals with the abstract-valued Orlicz spaces of range-varying type. Using notions of Banach space net and continuous modular net etc., we give definitions of Lϱθ(⋅)(I, Xθ(⋅)) and
L+ϱθ(⋅)$\begin{array}{}
L_{+}^{\varrho_{\theta(\cdot)}}
\end{array} $(I, Xθ(⋅)), and discuss their geometrical properties as well as the representation of
L+ϱθ(⋅)$\begin{array}{}
L_{+}^{\varrho_{\theta(\cdot)}}
\end{array} $(I, Xθ(⋅))*. We also investigate some functionals and operators on Lϱθ(⋅)(I, Xθ(⋅)), giving expression for the subdifferential of the convex functional generated by another continuous modular net. After making some investigations on the Bochner-Sobolev spaces W1, ϱθ(⋅)(I, Xθ(⋅)) and
Wper1,ϱθ(⋅)$\begin{array}{}
W_{\textrm{per}}^{1,\varrho_{\theta(\cdot)}}
\end{array} $(I, Xθ(⋅)), and the intersection space
Wper1,ϱθ(⋅)$\begin{array}{}
W_{\textrm{per}}^{1,\varrho_{\theta(\cdot)}}
\end{array} $(I, Xθ(⋅)) ∩ Lφϑ(⋅)(I, Vϑ(⋅)), a second order differential inclusion together with an anisotropic nonlinear elliptic equation with nonstandard growth are also taken into account. |
topic |
continuous modular net xθ(⋅)–valued function space geometrical property doubly nonlinear differential inclusion 46b10 46e30 46e40 |
url |
https://doi.org/10.1515/math-2018-0080 |
work_keys_str_mv |
AT zhangqinghua abstractvaluedorliczspacesofrangevaryingtype |
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1717777179414102016 |