Besov Space, Schatten Classes And Commutators Of Riesz Transforms Associated With The Neumann Laplacian

Abstract

This article provides a deeper study of the Riesz transform commutators associated with the Neumann Laplacian operator ${\Delta }_N$ on ${\mathbb{R}}^n$. Along the line of singular value estimates for Riesz transform commutators established by Janson--Wolff and Rochberg--Semmes, we establish a full range of Schatten-$p$ class characterization for these commutators.