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

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 Kantorovichs inequality. Some bounds for expectations of convex functions are also given in the multivariate case. Author