Taylor & Francis Group Generalized Hardy Operators and Normalizing Measures

Necessary and sufficient conditions on the weight v and the measure a for the operator b(s) k(s, y)f(y)dyKf(s) to be bounded from Lo[0 o) to Lq(s) are given. Here a(s) and b(s) are similarly ordered functions and k(s,y) 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