Mathematical Theory and Applications ›› 2024, Vol. 44 ›› Issue (1): 62-77.doi: 10.3969/j.issn.1006-8074.2024.01.005
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Liu Kaituo1, Yu Qian2,*
Online:
Published:
Abstract: In this paper, the inclusion of Musielak-Orlicz spaces is proved, which is a generalization of the inclusion of Orlicz spaces. Due to the fact that a variable exponent space is a special case of the Musielak-Orlicz space, we can obtain the equivalent relations of inclusion conditions between the spaces $L^{p(\cdot)}$ and $L^{q( \cdot)}$. At the same time, we get the inclusion of weighted Orlicz spaces. In addition, we also prove the inclusion of weak Musielak-Orlicz spaces, which is a generalization of weak variable exponent spaces. As applications, the equivalent relations of inclusion conditions between weak variable exponent spaces $wL^{p(\cdot)}$ and $wL^{q(\cdot)}$ and the inclusion of weak Orlicz spaces are established.
Key words: Musielak-Orlicz space , Weak Musielak-Orlicz space, Inclusion
Liu Kaituo, Yu Qian. Inclusion of Musielak-Orlicz Type Spaces[J]. Mathematical Theory and Applications, 2024, 44(1): 62-77.
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URL: http://mta.csu.edu.cn/EN/10.3969/j.issn.1006-8074.2024.01.005
http://mta.csu.edu.cn/EN/Y2024/V44/I1/62