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.
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