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On the convexity coefficient of Musielak–Orlicz function spaces equipped with the Orlicz norm

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  • Tianbao Guo
  • Yunan Cui

Abstract

In Hudzik and Landes, the convexity coefficient of Musielak–Orlicz function spaces over a non‐atomic measure space equipped with the Luxemburg norm is computed whenever the Musielak–Orlicz functions are strictly convex see [6]. In this paper, we extend this result to the case of Musielak–Orlicz spaces equipped with the Orlicz norm. Also, a characterization of uniformly convex Musielak–Orlicz function spaces as well as k‐uniformly convex Musielak–Orlicz spaces equipped with the Orlicz norm is given.

Suggested Citation

  • Tianbao Guo & Yunan Cui, 2023. "On the convexity coefficient of Musielak–Orlicz function spaces equipped with the Orlicz norm," Mathematische Nachrichten, Wiley Blackwell, vol. 296(8), pages 3344-3353, August.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:8:p:3344-3353
    DOI: 10.1002/mana.202100604
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