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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.
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