A Simple Proof of Inequalities of Integrals of Composite Functions

Details A Simple Proof of Inequalities of Integrals of Composite Functions A Simple Proof of Inequalities of Integrals of Composite Functions

2006-05-11

arxiv.org/abs/math/0605307v1

Journal of Mathematical Analysis and Applications, Vol 332, Number 2, 2007, p1308-1313.

Mathematics

Functional Analysis

Scientific paper

10.1016/j.jmaa.2006.11.007

In this paper we give a simple proof of inequalities of integrals of functions which are the composition of nonnegative continous convex functions on a vector space ${\bf R}^m$ and vector-valued functions in a weakly compact subset of a Banach vector space generated by $m$ $L_\mu^p$-spaces for $1\leq p<+\infty.$ Also, the same inequalities hold if these vector-valued functions are in a weakly* compact subset of a Banach vector space generated by $m$ $L_\mu^\infty$-spaces instead.

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