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Smoothness of the Orlicz Norm in Musielak-Orlicz Function Spaces (1404.4306v1)
Published 16 Apr 2014 in math.FA
Abstract: In this paper, we present a characterization of support functionals and smooth points in $L_{0}{\Phi}$, the Musielak-Orlicz space equipped with the Orlicz norm. As a result, criterion for the smoothness of $L_{0}{\Phi}$ is also obtained. Some expressions involving the norms of functionals in $(L_{0}{\Phi}){*}$, the topological dual of $L_{0}{\Phi}$, are proved for arbitrary Musielak-Orlicz functions.