Nuclearity and trace formulas of integral operators

Abstract

We present some results on the nuclearity (or trace class) of integral operators acting on $L^2(X,\nu )$ under specific conditions. These results improve and adapt a number of methods found in references on this subject. Our discussions take place within the context of special subsets (and manifolds) of the Euclidean space (endowed with weighted Lebesgue measure), second-countable spaces, and Lusin and Souslin spaces (endowed with $\sigma$-finite Borel measure).