A Simple Proof of Inequalities of Integrals of Composite Functions

Abstract

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 ${\mathbf{R}}^m$ and vector-valued functions in a weakly compact subset of a Banach vector space generated by $m$ $L_{\mu }^p$-spaces for $1\le p<+\infty .$ 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.

Cited by in corpus (1)

• The Banach-Saks Property of the Banach Product Spaces