Abstract
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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Schappacher, G. A Notion of Orlicz Spaces for Vector Valued Functions. Appl Math 50, 355–386 (2005). https://doi.org/10.1007/s10492-005-0028-9
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DOI: https://doi.org/10.1007/s10492-005-0028-9