Regular Banach space net and abstract-valued Orlicz space of range-varying type

• Main Authors: Zhang Qinghua, Zhu Yueping
• Format: Article
• Language: English
• Published: De Gruyter 2019-12-01
• Series: Open Mathematics
• Subjects: banach space net; partially continuous modular net; range-varying orlicz space; real interpolation space; 46b10; 46e30; 46e40
• Online Access: http://www.degruyter.com/view/j/math.2019.17.issue-1/math-2019-0130/math-2019-0130.xml?format=INT

This paper investigates the abstract-valued Orlicz space of range-varying type. We firstly give the notions and examples of partially continuous modular net and regular Banach space net of type (II), then deal with the definitions, constructions, and geometrical properties of the range-varying Orlicz spaces, including representation of the dual L+φ$\begin{array}{} L_{+}^{\varphi} \end{array}$(I, Xθ(⋅))*, and reflexivity of Lφ(I, Xθ(⋅)), under some reasonable conditions. As an application, we finally make another approach to the real interpolation spaces constructed by a generalized Φ-function.