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vector valued function; Orlicz space; Luxemburg norm; delta-growth condition; duality
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.
[1] J.  Lemaitre, J.-L. Chaboche: Mechanics of Solid Materials. Cambridge University Press, Cambridge, 1990.
[2] J.-P.  Aubin: Optima and Equilibria. An Introduction to Nonlinear Analysis. Springer-Verlag, Berlin, 1998. MR 1729758 | Zbl 0930.91001
[3] W.  Desch, R.  Grimmer: On the well-posedness of constitutive laws involving dissipation potentials. Trans. Am. Math. Soc. 353 (2001), 5095–5120. DOI 10.1090/S0002-9947-01-02847-1 | MR 1852096
[4] M. M. Rao, Z. D. Ren: Theory of Orlicz Spaces. Pure and Applied Mathematics, Vol. 146. Marcel Dekker, New York, 1991. MR 1113700
[5] M. A. Krasnosel’skij, Ya. B.  Rutickij: Convex Functions and Orlicz Spaces. P.  Noordhoff, Groningen, 1961. MR 0126722
[6] J.  Musielak: Orlicz Spaces and Modular Spaces. Lecture Notes in Mathematics  1034, Springer-Verlag, Berlin, 1983. MR 0724434 | Zbl 0557.46020
[7] M. S.  Skaff: Vector valued Orlicz spaces. Generalized $N$-functions, I. Pac. J.  Math. 28 (1969), 193–206. DOI 10.2140/pjm.1969.28.193 | MR 0415305 | Zbl 0176.11002
[8] M. S. Skaff: Vector valued Orlicz spaces, II. Pac. J.  Math. 28 (1969), 413–430. DOI 10.2140/pjm.1969.28.413 | MR 0415306 | Zbl 0176.11003
[9] G. Schappacher: Generalizations of Orlicz spaces of vector valued functions. PhD. Thesis, Karl Franzens University, Graz, 2003. MR 2151462
[10] C. Bennett, R.  Sharpley: Interpolation of Operators. Pure and Applied Mathematics, Vol. 129. Academic Press, Boston, 1988. MR 0928802
[11] N.  Dinculeanu: Vector Measures. Hochschulbücher für Mathematik. Pergamon Press, VEB Deutscher Verlag der Wissenschaften, Berlin, 1966. (English) MR 0206189
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