A counterexample to weighted estimates for multilinear Fourier multipliers with Sobolev regularity

TL;DR

This paper investigates whether weighted estimates for multilinear Fourier multipliers with Sobolev regularity are valid under weak weight conditions, challenging existing assumptions in harmonic analysis.

Contribution

It provides a counterexample showing that such weighted estimates do not always hold under minimal weight conditions.

Findings

Counterexample disproves general weighted estimates

Highlights limitations of Sobolev regularity assumptions

Suggests need for stronger conditions on weights

Abstract

The problem whether weighted estimates for multilinear Fourier multipliers with Sobolev regularity hold under weak condition on weights is considered.