Generalized Hardy operators and normalizing measures

Abstract

Necessary and sufficient conditions on the weight and the measure for the operator to be bounded from to are given. Here and are similarly ordered functions and satisfies a modified GHO condition. Nearly block diagonal decompositions of positive operators are introduced as is the concept of a normalizing measure. An application is made to estimates for the remainder in a Taylor approximation.

Keywords

• Hardy inequality
• Weight
• Normalizing measure