Maximal operator for the higher order Calderón commutator

Abstract

In this paper, we investigate the weighted multilinear boundedness properties of the maximal higher order Calderón commutator for the dimensions larger than two. We establish all weighted multilinear estimates on the product of the $L^p({\mathbb{R}}^d,w)$ space, including some peculiar endpoint estimates of the higher dimensional Calderón commutator.

36 pages, Canadian Journal of Mathematics, to appear. arXiv admin note: text overlap with arXiv:1712.09020