I-convexity and Q-convexity of Orlicz-Bochner function spaces with the Luxemburg norm
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摘要: 根据Banach空间中I-凸与Q-凸的等价定义得到了当
$(\Omega,\Sigma,\mu)$ 为有限测度空间时, Luxemburg范数下Orlicz-Bochner函数空间$L_{(M)}(\mu, X)$ 为I-凸的当且仅当$M\in{\Delta}_2(\infty)\cap$ $ {\nabla}_2(\infty)$ , 且$X$ 为I-凸的;$L_{(M)}(\mu,X)$ 为Q-凸的当且仅当$M\in{\Delta}_2(\infty)\cap{\nabla}_2(\infty)$ , 且$X$ 为Q-凸的.-
关键词:
- I-凸性 /
- Q-凸性 /
- Luxemburg范数 /
- Orlicz-Bochner函数空间
Abstract: There are some equivalent definitions for I-convexity and Q-convexity. In this context, if$(\Omega,\Sigma,\mu)$ is a finite measure space, the Orlicz-Bochner function space$L_{(M)}(\mu,X)$ endowed with the Luxemburg norm is I-convex if and only if$M\in{\Delta}_2(\infty)\cap{\nabla}_2(\infty)$ and$X$ is I-convex; similarly,$L_{(M)}(\mu,X)$ is Q-convex if and only if$M\in{\Delta}_2(\infty)\cap{\nabla}_2(\infty)$ and$X$ is Q-convex.-
Key words:
- I-convexity /
- Q-convexity /
- Luxemburg norm /
- Orlicz-Bochner function space
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