A lower bound criterion for iterated commutators

International audienceWe consider iterated commutators of multiplication by a symbol function and smooth Calder on-Zygmund operators, described by Fourier multipliers of homogeneity 0. We establish a criterion for a collection of symbols so that the corresponding Calder on-Zygmund operators characterize product BMO by means of iterated commutators. We therefore ex- tend, in part, the line of one-parameter results following the work of Uchiyama and Li as well as the result in several parameters, concerning commutators with Riesz transforms by Lacey, Petermichl, Pipher, Wick