# Boundedness and Compactness of commutator of Hardy-Littlewood maximal operator

## TL;DR

This paper investigates the boundedness and compactness properties of the commutator of the bilinear Hardy-Littlewood maximal operator within homogeneous Triebel-Lizorkin spaces, revealing new results even in the linear case.

## Contribution

It establishes the boundedness and compactness of the commutator operator, providing new insights in both bilinear and linear settings.

## Key findings

- The commutator is bounded on certain function spaces.
- The commutator acts as a compact operator on product Lebesgue spaces.
- Results are novel even for the linear 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.

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Source: https://tomesphere.com/paper/1706.06242