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

This article provides a deeper study of the Riesz transform commutators associated with the Neumann Laplacian operator ${\mathrm{\Delta }}_N$ 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.