Embeddedness, Compactness and Uniform Convexity of Anisotropic Banach Space Valued Musielak-Orlicz Spaces

doi:10.3969/j.issn.1006-8074.2024.01.004

Mathematical Theory and Applications ›› 2024, Vol. 44 ›› Issue (1): 45-61.doi: 10.3969/j.issn.1006-8074.2024.01.004

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Embeddedness, Compactness and Uniform Convexity of Anisotropic Banach Space Valued Musielak-Orlicz Spaces

He Yali¹ , Xu Jingshi^2,*

1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China; 2. Center for Applied Mathematics of Guangxi, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China

Online:2024-03-28 Published:2024-04-16
Contact: Xu Jingshi (1966–), Professor, PhD; E-mail: jingshixu@126.com
Supported by:
This work is supported by the National Natural Science Foundation of China (No. 12161022

Abstract

Abstract: In this paper we give the necessary and sufficient conditions for the embedding of an anisotropic Banach space valued Musielak-Orlicz space into another anisotropic Banach space valued Musielak-Orlicz space, and the necessary and sufficient conditions for a subset of an anisotropic Banach space valued Musielak-Orlicz space to be relatively compact, and characterize the uniform convexity of anisotropic Banach space valued Musielak-Orlicz space.

Key words: Banach space valued Musielak-Orlicz space, Embeddedness, Compactness, Uniform convexity

He Yal, Xu Jingshi. Embeddedness, Compactness and Uniform Convexity of Anisotropic Banach Space Valued Musielak-Orlicz Spaces[J]. Mathematical Theory and Applications, 2024, 44(1): 45-61.

Embeddedness, Compactness and Uniform Convexity of Anisotropic Banach Space Valued Musielak-Orlicz Spaces

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