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Title: A notion of Orlicz spaces for vector valued functions (English)
Author: Schappacher, Gudrun
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 50
Issue: 4
Year: 2005
Pages: 355-386
Summary lang: English
Category: math
Summary: The notion of the Orlicz space is generalized to spaces of Banach-space valued functions. A well-known generalization is based on $N$-functions of a real variable. We consider a more general setting based on spaces generated by convex functions defined on a Banach space. We investigate structural properties of these spaces, such as the role of the delta-growth conditions, separability, the closure of $\mathcal L^{\infty }$, and representations of the dual space. (English)
Keyword: vector valued function
Keyword: Orlicz space
Keyword: Luxemburg norm
Keyword: delta-growth condition
Keyword: duality
MSC: 46B10
MSC: 46E30
MSC: 46E40
idZBL: Zbl 1099.46021
idMR: MR2151462
DOI: 10.1007/s10492-005-0028-9
Date available: 2009-09-22T18:22:58Z
Last updated: 2020-07-02
Stable URL:
Reference: [1] J.  Lemaitre, J.-L. Chaboche: Mechanics of Solid Materials.Cambridge University Press, Cambridge, 1990.
Reference: [2] J.-P.  Aubin: Optima and Equilibria. An Introduction to Nonlinear Analysis.Springer-Verlag, Berlin, 1998. Zbl 0930.91001, MR 1729758
Reference: [3] W.  Desch, R.  Grimmer: On the well-posedness of constitutive laws involving dissipation potentials.Trans. Am. Math. Soc. 353 (2001), 5095–5120. MR 1852096, 10.1090/S0002-9947-01-02847-1
Reference: [4] M. M. Rao, Z. D. Ren: Theory of Orlicz Spaces. Pure and Applied Mathematics, Vol. 146.Marcel Dekker, New York, 1991. MR 1113700
Reference: [5] M. A. Krasnosel’skij, Ya. B.  Rutickij: Convex Functions and Orlicz Spaces.P.  Noordhoff, Groningen, 1961. MR 0126722
Reference: [6] J.  Musielak: Orlicz Spaces and Modular Spaces.Lecture Notes in Mathematics  1034, Springer-Verlag, Berlin, 1983. Zbl 0557.46020, MR 0724434
Reference: [7] M. S.  Skaff: Vector valued Orlicz spaces. Generalized $N$-functions, I.Pac. J.  Math. 28 (1969), 193–206. Zbl 0176.11002, MR 0415305, 10.2140/pjm.1969.28.193
Reference: [8] M. S. Skaff: Vector valued Orlicz spaces, II.Pac. J.  Math. 28 (1969), 413–430. Zbl 0176.11003, MR 0415306, 10.2140/pjm.1969.28.413
Reference: [9] G. Schappacher: Generalizations of Orlicz spaces of vector valued functions.PhD. Thesis, Karl Franzens University, Graz, 2003. MR 2151462
Reference: [10] C. Bennett, R.  Sharpley: Interpolation of Operators. Pure and Applied Mathematics, Vol. 129.Academic Press, Boston, 1988. MR 0928802
Reference: [11] N.  Dinculeanu: Vector Measures. Hochschulbücher für Mathematik.Pergamon Press, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. (English) MR 0206189


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