Journal of Inequalities and Applications 
Volume 3 (1999), Issue 3, Pages 245-266
doi:10.1155/S1025583499000168

An integral operator inequality with applications

R. S. Chisholm,1 W. N. Everitt,2 and L. L. Littlejohn3

 1Swisscom Ltd., Department PD53, Viktoriastrasse 21, Bern 3050, Switzerland
2School of Mathematics and Statistics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
3Department of Mathematics and Statistics, Utah State University, Logan 84322-3900, UT, USA
Received 15 June 1998; Revised 6 July 1998

Abstract

Linear integral operators are defined acting in the Lebesgue integration spaces on intervals of the real line. A necessary and sufficient condition is given for these operators to be bounded, and a characterisation is given for the operator bounds. There are applications of the results to integral inequalities; also to properties of the domains of self-adjoint unbounded operators, in Hilbert function spaces, associated with the classical orthogonal polynomials and their generalisations.