# Multilinear BMO estimates for the commutators of multilinear fractional maximal and integral operators on the product generalized Morrey spaces

## TL;DR

This paper develops multilinear BMO estimates for commutators of fractional maximal and integral operators on product generalized Morrey spaces, extending the theory to vanishing spaces and related operators.

## Contribution

It introduces new multilinear BMO estimates for commutators on generalized Morrey spaces, including vanishing spaces, and applies to maximal and singular integral operators.

## Key findings

- Established multilinear BMO estimates on product generalized Morrey spaces.
- Extended results to product generalized vanishing Morrey spaces.
- Applicable to commutators of maximal and singular integral operators.

## Abstract

In this paper, we establish multilinear BMO estimates for commutators of multilinear fractional maximal and integral operators both on product generalized Morrey spaces and product generalized vanishing Morrey spaces, respectively. Similar results are still valid for commutators of multilinear maximal and singular integral operators.