赋Orlicz范数的Orlicz-Lorentz空间的严格凸性

STRICT CONVEXITY OF ORLICZ LORENTZ SPACES WITH ORLICZ NORM

本文对于赋Ｌｕｘｅｍｂｕｒｇ范数的Ｏｒｌｉｃｚ－Ｌｏｒｅｎｔｚ空间（∧φ，ｗ，‖·‖），引进了一种与Ｌｕｘｅｍｂｕｒｇ范数等价的新的范数（记为‖·‖０），称之为Ｏｒｌｉｃｚ范数，并且给出了Ｏｒｌｉｃｚ－Ｌｏｒｅｎｔｚ空间∧φ，ｗ关于Ｏｒｌｉｃｚ范数严格凸的充要条件。

In this paper, we introduce Orlicz norm which is equivalent to Luxemburg norm in Orlicz Lorentz spaces. And then, we give a criterion for strict convexity of Orlicz Lorentz spaces equipped with Orlicz norm. This provides a new frame for studying geometric properties of Orlicz Lorentz spaces.