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.
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 Science), 2020
, 2020(1)
: 40
-50
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DOI: 10.3969/j.issn.1000-5641.201811042
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