A simple proof of inequalities of integrals of composite functions |
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| Authors: | Zhenglu Jiang Xiaoyong Fu |
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| Affiliation: | a Department of Mathematics, Zhongshan University, Guangzhou 510275, China
b Department of Mathematics, Shanghai Teachers' University, Shanghai 200234, China |
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| Abstract: | 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 Rm and vector-valued functions in a weakly compact subset of a Banach vector space generated by m -spaces for 1?p<+∞. Also, the same inequalities hold if these vector-valued functions are in a weakly* compact subset of a Banach vector space generated by m -spaces instead. |
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| Keywords: | Convex functions Measure spaces Lebesgue integrals Banach spaces |
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