Weighted estimates for multilinear Fourier multipliers

TL;DR

This paper establishes a Hörmander-type theorem for multilinear Fourier multipliers with multiple weights and provides weighted estimates for their commutators involving vector BMO functions.

Contribution

It introduces a new weighted multiplier theorem for multilinear Fourier multipliers and analyzes their commutators with BMO functions.

Findings

Proved a Hörmander-type theorem for weighted multilinear Fourier multipliers.

Derived weighted estimates for commutators with vector BMO functions.

Extended multiplier theory to multiple weights in a multilinear setting.

Abstract

We prove a H\"{o}rmander type multiplier theorem for multilinear Fourier multipiers with multiple weights. We also give weighted estimates for their commutators with vector $BMO$ functions.