Schatten-von Neumann classes of integral operators

Understand

In this work we establish sharp kernel conditions ensuring that the corresponding integral operators belong to Schatten-von Neumann classes.

• The conditions are given in terms of the spectral properties of operators acting on the kernel.
• As applications we establish several criteria in terms of different types of differential operators and their spectral asymptotics in different settings: compact manifolds, operators on lattices, domains in ${\mathbb R}^n$ of finite measure, and conditions for operators on ${\mathbb R}^n$ given in terms of anharmonic oscillators.
• We also give examples in the settings of compact sub-Riemannian manifolds, contact manifolds, strictly pseudo-convex CR manifolds, and (sub-)Laplacians on compact Lie groups.