I-convexity and Q-convexity of Orlicz-Bochner function spaces with the Luxemburg norm

DONG Xiaoli; GONG Wanzhong

doi:10.3969/j.issn.1000-5641.201811042

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DONG Xiaoli, GONG Wanzhong. I-convexity and Q-convexity of Orlicz-Bochner function spaces with the Luxemburg norm[J]. Journal of East China Normal University (Natural Sciences), 2020, (1): 40-50. doi: 10.3969/j.issn.1000-5641.201811042

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DONG Xiaoli, GONG Wanzhong. I-convexity and Q-convexity of Orlicz-Bochner function spaces with the Luxemburg norm[J]. Journal of East China Normal University (Natural Sciences), 2020, (1): 40-50. doi: 10.3969/j.issn.1000-5641.201811042

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I-convexity and Q-convexity of Orlicz-Bochner function spaces with the Luxemburg norm

doi: 10.3969/j.issn.1000-5641.201811042

DONG Xiaoli,
GONG Wanzhong^,

School of Mathematics and Statistics, Anhui Normal University, Wuhu Anhui　241000, China

Received Date: 2018-11-13
Available Online: 2019-12-25
Publish Date: 2020-01-01

Abstract

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.
- I-convexity,
- Q-convexity,
- Luxemburg norm,
- Orlicz-Bochner function space

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References(16)

References

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