Journal of Inequalities and Applications
Volume 7 (2002), Issue 6, Pages 829-866
doi:10.1155/S1025583402000437
Generalized Hardy operators and normalizing measures
Department of Mathematics, University of Western Ontario, Ontario, London N6A 5B7, Canada
Received 15 February 2001; Revised 1 May 2001
Copyright © 2002 Tieling Chen and Gord Sinnamon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.