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 ${\mathrm{\Delta }}_{\mathit{N}}$ on ${\mathbb{R}}^{\mathit{n}}$. Along the line of singular value estimates for Riesz transform commutators established by Janson and Wolff and Rochberg and Semmes, we establish a full range of Schatten-p class characterization for these commutators.