Eigenvalue decay rates for positive integral operators

Abstract

We present decay rates for the eigenvalues of positive integral operators with smooth kernels on special metric spaces endowed with a strictly positive measure. The smoothness is defined by either differentiability conditions or inequalities of Lipschitz type. We use the decay rates to place the operators in some Schatten p-classes. © 2012 Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag.