赋Orlicz范数的Orlicz-Bochner空间E_M(μ,X)的对偶空间

THE DUAL SPACE OF ORLICZ-BOCHNER SPACE EM(μ,X) WITH ORLICZ NORM

本文研究了Orlicz-Bochner空间EM（μ,X）的对偶空间的充分必要条件.运用Radon-Nikodym性质,给出Orlicz-Bochner空间L（N）（μ,X^＊）为EM（μ,X）^＊的对偶空间当且仅当X^＊具Radon-Nikodym性质,提升了Orlicz空间及Lebesgue-Bochner空间的相关结论.

In this article, we study the dual space of Orlicz-Bochner space EM（μ, X）. Using Radon-Nikodym property, we give that Orlicz-Bochner space L（N）（μ, X^＊） is the dual space of EM（μ, X）^＊ if and only if X^＊ has Radon-Nikodym property. Hence we improve the interrelated resluts in Orlicz space and Lebesgue-Bochner space.