Geodesic
A notion of Orlicz spaces for vector valued functions
Applications of Mathematics, Tome 50 (2005) no. 4, pp. 355-386
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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.
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.
DOI : 10.1007/s10492-005-0028-9
Classification : 46B10, 46E30, 46E40
Keywords: vector valued function; Orlicz space; Luxemburg norm; delta-growth condition; duality 
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Schappacher, Gudrun. A notion of Orlicz spaces for vector valued functions. Applications of Mathematics, Tome 50 (2005) no. 4, pp. 355-386. doi: 10.1007/s10492-005-0028-9

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