Differentiated Shift Invariant Multivariate Integral Operators

Abstract

This is a continuation of Chapter 11, among others, we still study global smoothness preservation over R ^d,d > 1. Here are given sufficient conditions, so that the partial derivatives of general multivariate operators, examined in Chapter 11, enjoy most of the nice properties of their originals. Especially a sufficient condition is given so that the “global smoothness preservation” corresponding multivariate inequality is attained, that is sharp. Finally several applications are given, there the partial derivatives of very general specialized multivariate operators are shown to fulfill most of in Chapter 11 mentioned properties. In particular the partials of these operators are shown to preserve continuous multivariate probability density functions. Here we follow the basic study [20].