关键词: Musielak-Orlicz 空间, 弱 Musielak-Orlicz 空间, 嵌入关系

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