Let (Ω,μ) be a a-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...Let (Ω,μ) be a a-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).展开更多
基金Project supported by National Natural Science Foundation of China(10371052,10671084)
文摘Let (Ω,μ) be a a-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).