Mixed means of commutators of central integral means and CMO

TL;DR

This paper develops mixed means and weighted $L^p$ estimates for commutators of central integral means operators involving $CMO$ functions, advancing the understanding of their boundedness and behavior.

Contribution

It introduces new mixed means and weighted $L^p$ estimates for higher-order commutators with $CMO$ functions, extending previous results in harmonic analysis.

Findings

Established weighted $L^p$ bounds for commutators

Derived new mixed mean inequalities

Analyzed the behavior of higher-order central integral means

Abstract

In this paper we obtain some mixed means and weighted $L^p$ estimates for the commutators generating $r$ order central integral means operators with $CMO$ functions.