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

doi:10.3969/j.issn.1000-5641.201811042

Abstract

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

CLC Number:

O177.2

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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