Abstract
Abstract In this paper, we first introduce the new class of multiple weights A p → ∞ ${A^\infty _{\vec{p}}}$ which is larger than the class of multiple weights in [Adv. Math. 220 (2009), 1222–1264]. 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 in [J. Fourier Anal. Appl. 17 (2011), 115–134]. Finally, we show that some multilinear pseudodifferential operators fall within the scope of the theory obtained in this paper.
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