A simple proof of inequalities of integrals of composite functions

作者：Jiang, Zhenglu^*; Fu, Xiaoyong; Tian, Hongjiong

来源：Journal of Mathematical Analysis and Applications, 2007, 332(2): 1308-1313.

DOI：10.1016/j.jmaa.2006.11.007

• convex functions
• measure spaces
• Lebesgue integrals
• Banach spaces

In this paper we give a simple proof of inequalities of integrals of functions which are the composition of nonnegative continuous convex functions on a vector space R-m and vector-valued functions in a weakly compact subset of a Banach vector space generated by m L-mu(p)-spaces for 1 <=, p < infinity. Also, the same inequalities hold if these vector-valued functions are in a weakly* compact subset of a Banach vector space generated by m L-mu(p)-spaces instead.

• 出版日期2007-8-15
• 单位上海师范大学; 中山大学