# Two-weight commutator estimates: general multi-parameter framework

## TL;DR

This paper develops a comprehensive framework for establishing two-weight commutator estimates in multi-parameter settings, extending prior results to arbitrary parameters and clarifying existing literature.

## Contribution

It introduces a general technical framework for multi-parameter two-weight commutator estimates, broadening the scope beyond previous two-parameter-focused results.

## Key findings

- Established explicit multi-parameter two-weight commutator estimates
- Extended Bloom type estimates to arbitrary parameters
- Clarified the theoretical structure of weighted BMO spaces

## Abstract

We provide an explicit technical framework for proving very general two-weight commutator estimates in arbitrary parameters. The aim is to both clarify existing literature, which often explicitly focuses on two parameters only, and to extend very recent results to the full generality of arbitrary parameters. More specifically, we study two-weight commutator estimates -- Bloom type estimates -- in the multi-parameter setting involving weighted product BMO and little BMO spaces, and their combinations.