Journal of East China Normal University(Natural Science) ›› 2020, Vol. 2020 ›› Issue (1): 40-50.doi: 10.3969/j.issn.1000-5641.201811042

• Mathematics • Previous Articles     Next Articles

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

DONG Xiaoli, GONG Wanzhong   

  1. School of Mathematics and Statistics, Anhui Normal University, Wuhu Anhui 241000, China
  • Received:2018-11-13 Published:2020-01-13

Abstract: There are some equivalent definitions for I-convexity and Q-convexity. In this context, if (Ω, Σ, μ) is a finite measure space, the Orlicz-Bochner function space L(M)(μ, X) endowed with the Luxemburg norm is I-convex if and only if M ∈ △2(∞) ∩ ▽2(∞) and X is I-convex; similarly, L(M)(μ, X) is Q-convex if and only if M ∈ △2(∞) ∩ ▽2(∞) and X is Q-convex.

Key words: I-convexity, Q-convexity, Luxemburg norm, Orlicz-Bochner function space

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