赋广义Orlicz范数的Orlicz函数空间的一致凸性

Uniform Rotundity in Orlicz Function Spaces Equipped with Generalized Orlicz Norm

利用Banach及经典Orlicz空间几何理论,研究赋广义Orlicz范数的Orlicz函数空间一致凸问题,得到了由右导函数为凸函数的N-函数生成的赋广义Orlicz范数的Orlicz函数空间一致凸的充要条件.

By means of geometries of Banach spaces and Orlicz spaces method,the characterizations over uniform rotundity of the Orlicz function spaces equipped with the generalized Orlicz norm was discussed.For the Orlicz function spaces generated by a N-function whose derivative on the right is convex and equipped with the generalized Orlicz norm,both sufficient and necessary conditions were presented to make them be uniform rotund.