Boundedness and Compactness of commutator of Hardy-Littlewood maximal operator

Abstract

We study the mapping property of the commutator of bilinear Hardy-Littlewood maximal operator in homogeneous Triebel-Lizorkin space. We also show that the commutator of bilinear Hardy-Littlewood maximal operator is a compact operator acting on product of Lebesgue spaces. The results are new even in the linear case.

An error has occurred: The classical Kolmogorov result about characterization of compactness is usually applied with linear operators. Unfortunately, commutator of Hardy-Littlewood maximal operator is a sublinear one