Abstract:There is given a criterion for an arbitrary element from the unit sphere of Musielak-Orlicz function space equipped with the Luxemburg norm to be a point of smoothness. Next, as a corollary, a criterion of smoothness of these spaces is given.
Keywords: Musielak-Orlicz function, Musielak-Orlicz space, support functional, smooth point, smooth space
AMS Subject Classification: Primary 46E30; Secondary 45B20