向量值Musielak-Orlicz空间的两种几何性质(英)

Two Geometrical Properties of Vector-Valued Musielak-Orlicz Spaces

设Ｘ是复Ｂａｎｃｈ空间，Ｍ（ｔ，ｕ）是以ｔ为参数的满足某些通常条件的Φ－函数．我们证明了；（ｉ）Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ空间Ｌ_Ｍ（Ｘ）具有解析ＵＭＤ性质当且仅当Ｘ具有；（ｉｉ） Ｌ_Ｍ（Ｘ）具有解析ＲＮ性质当且仅当Ｘ具有．

Let X be a complex Banach space and M(t,u) a Φ－function with parameter t satisfing some usual conditions. We proved: (i) The Musielak-Orlicz space L_M (X) is an analytic UMD space if and only if X is an analytic UMD space, too. ii) L_M(X) has the analytic RN property if and only X does.