Sparse domination theorem for multilinear singular integral operators with $L^{r}$-H\"ormander condition

TL;DR

This paper proves that multilinear singular integral operators satisfying an $L^{r}$-H"ormander condition can be controlled by sparse operators, advancing the understanding of their boundedness properties.

Contribution

It establishes a sparse domination theorem for multilinear operators under the $L^{r}$-H"ormander condition, a new criterion in the field.

Findings

Multilinear operators can be dominated by sparse operators under the $L^{r}$-H"ormander condition.

Provides a new approach to analyze boundedness of multilinear singular integrals.

Extends sparse domination techniques to a broader class of kernels.

Abstract

In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the so-called multilinear $L^{r}$-H\"ormander condition, then $T$ can be dominated by multilinear sparse operators.