Smoothness of the Orlicz Norm in Musielak-Orlicz Function Spaces

摘要

In this paper, we present a characterization of support functionals andsmooth points in $L_{0}^{\Phi}$, the Musielak-Orlicz space equipped with theOrlicz norm. As a result, criterion for the smoothness of $L_{0}^{\Phi}$ isalso obtained. Some expressions involving the norms of functionals in$(L_{0}^{\Phi})^{*}$, the topological dual of $L_{0}^{\Phi}$, are proved forarbitrary Musielak-Orlicz functions.