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Amemiya Norm Equals Orlicz Norm in Musielak–Orlicz Spaces

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Abstract

Let (Ω, μ) be a σ-finite measure space and Φ : Ω × [0,∞) → [0,∞] be a Musielak–Orlicz function. Denote by L Φ(Ω) the Musielak–Orlicz space generated by Φ. We prove that the Amemiya norm equals the Orlicz norm in L Φ(Ω).

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Authors and Affiliations

  1. Department of Mathematics, Lanzhou University, Lanzhou 730000, P. R. China

    Xian Ling Fan

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  1. Xian Ling Fan
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Correspondence to Xian Ling Fan.

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Project supported by National Natural Science Foundation of China (10371052, 10671084)

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Fan, X.L. Amemiya Norm Equals Orlicz Norm in Musielak–Orlicz Spaces. Acta Math Sinica 23, 281–288 (2007). https://doi.org/10.1007/s10114-005-0865-1

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  • DOI: https://doi.org/10.1007/s10114-005-0865-1

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