REVERSAL OF THE LYAPUNOV, HOLDER, AND MINKOWSKI INEQUALITIES AND OTHER EXTENSIONS OF THE KANTOROVICH INEQUALITY

摘要

Many classical inequalities — which involve random variables or functions on a measure space — can be "reversed" if bounds on the random variables or functions are known. This reversal is accomplished by ' introducing on one side of the inequality an appropriate multiplicative constant which depends on the known bounds. In this paper, several such inequalities are obtained, and a matrix-theoretic interpretation is used to yield various generalizations of Kantorovich's inequality. Some bounds for expectations of convex functions are also given in the multivariate case.