Journal of Inequalities and Applications 
Volume 7 (2002), Issue 6, Pages 829-866
doi:10.1155/S1025583402000437

Generalized Hardy operators and normalizing measures

Tieling Chen and Gord Sinnamon

 Department of Mathematics, University of Western Ontario, Ontario, London N6A 5B7, Canada
Received 15 February 2001; Revised 1 May 2001

Abstract

Necessary and sufficient conditions on the weight v and the measure σ for the operator Kf(s)=∫a(s)b(s)k(s,y)f(y)dy to be bounded from Lvp[0,∞) to Lσq(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.