Hilbert空间上凸函数的上、下指数的共轭性质

Conjugate Properties of the Super (Lower) Exponent Convex Function on Hilbert Spaces

本文引入Ｈｉｌｂｅｒｔ空间上非负凸函数具有一般性的上下指数的概念，得到相互共轭凸函数的上下指数的共轭性质，也讨论了由内积范数导出的正ｐ（ｐ＞１）次齐次函数与正ｑ（ｑ＞１。

In this paper,a general concept of the super (lower) exponent of non-negative convex function on Hilbert spaces is introduced. Conjugate properties of the super(lower) exponent for mutually conjugate convex function are obtained,the relation of the positive p(p>1) order homogeneous function and positive q(q>1,1p+1q=1) order homogeneous function are introduced by norms is considered also.