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Keywords:
generalized Orlicz space $L^{(M^{-1})}$; sequentially compact set; $\triangle_2$-condition
generalized Orlicz space $L^{(M^{-1})}$; sequentially compact set; $\triangle_2$-condition
Summary:
In this paper, we will characterize sequentially compact sets in a class of generalized Orlicz spaces.
References:
[1] Rao M.M., Ren Z.D.: Theory of Orlicz Spaces. Marcel Dekker, New York, 1991. MR 1113700 | Zbl 0724.46032
[2] Maligranda L.: Orlicz Spaces and Interpolation. Seminars in Mathematics 5, Univ. Estadual de Campinas, Capinas SP Brasil, 1989. MR 2264389 | Zbl 0874.46022
[3] Rao M.M., Ren Z.D.: Applications of Orlicz Spaces. Marcel Dekker, New York, 2001, to appear. MR 1890178 | Zbl 0997.46027
[4] Riesz F.: Untersuchungen über Systeme integrierbarer Funktionen. Math. Ann. 69 (1910), 449-497. MR 1511596
[5] Kantorovich L.V., Akilov G.P.: Functional Analysis. Pergamon Press, New York, 1982. MR 0664597 | Zbl 0555.46001
[6] Krasnosel'skii M.A., Rutickii Ya.B.: Convex Functions and Orlicz Space. Noordhoff Ltd. Groningen, 1961. MR 0126722
[7] Takahashi T.: On the compactness of the function-set by the convergence in mean of general type. Studia Math. 5 (1935), 141-150. Zbl 0013.06501
[8] Gribanov Yu.: Nonlinear operators in Orlicz spaces (in Russian). U ̆c. zap. kazansk. Unta 115 (7) (1955).
[9] Tsuji M.: On the compactness of space $L^p(p>0)$ and its application to integral equation. Mathematical Institute, Tokyo University, 1951. Zbl 0044.10701
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