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00925njm 22002777a 4500 dc Lerner, Andrei author Ombrosi, Sheldy J. author Rivera Ríos, Israel P. author 2021 In this paper we extend the bump conjecture and a particular case of the separated bump conjecture with logarithmic bumps to iterated commutators . Our results are new even for the first order commutator . A new bump type necessary condition for the two-weighted boundedness of is obtained as well. We also provide some results related to a converse to Bloom's theorem. J. Funct. Anal. 281 (2021), no. 8, 109153 https://hdl.handle.net/10630/35574 10.1016/j.jfa.2021.109153 Calderón-Zygmund, Operadores de On two weight estimates for iterated commutators.