New class of multiple weights and new weighted inequalities for multilinear operators

TL;DR

This paper introduces a broader class of multiple weights for multilinear operators, establishing new weighted inequalities and applying them to pseudodifferential operators, advancing the understanding of weighted harmonic analysis.

Contribution

It defines a new class of multiple weights larger than previous ones and derives associated weighted inequalities for multilinear operators and their commutators.

Findings

New class of multiple weights $A^ extbf{vc}_{ extbf{p}}$ introduced

Weighted inequalities established for multilinear operators

Application to multilinear pseudodifferential operators

Abstract

In this paper, we first introduce the new class of multiple weights $A^\vc_{\vec{p}}$ which is larger than the class of multiple weights in \cite{LOPTG}. Then, using this class of weights, we study the weighted norm inequalities for certain classes of multilinear operators and their commutators with new BMO functions introduced by \cite{BHS1}. Finally, we show that some multilinear pseudodifferential operators fall within the scope of the theory obtained in this paper.