Weighted norm inequalities for multilinear singular integral operators and applications

TL;DR

This paper establishes weighted norm inequalities for multilinear singular integral operators with $A_p$ weights, extending previous results and providing new weighted estimates for multilinear Fourier multipliers.

Contribution

It introduces new weighted norm inequalities for multilinear singular integrals with $L^{r'}$-H"ormander regularity, and derives novel weighted estimates for multilinear Fourier multipliers.

Findings

Recovered a weighted estimate for multilinear Fourier multipliers

Established $A_p$ weighted inequalities for multilinear singular integrals

Provided new bounds for multilinear Fourier multipliers

Abstract

In this paper, weighted norm inequalities with $A_p$ weights are established for the multilinear singular integral operators whose kernels satisfy $L^{r'}$-H\"ormander regularity condition. As applications, we recover a weighted estimate for the multilinear Fourier multiplier obtained by Fujita and Tomita, and obtain several new weighted estimates for the multilinear Fourier multiplier as well.