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We investigate the construction of Carleson measures from families of multilinear integral operators applied to tuples of and BMO functions. We show that if the family of multilinear operators has cancellation in each variable, then for BMO functions b₁, ..., bₘ, the measure is Carleson. However, if the family of multilinear operators has cancellation in all variables combined, this result is still valid if are functions, but it may fail if are unbounded BMO functions, as we indicate...
We provide a modification for part of the proof of Theorem 1.2 of our article, pages 85-89, under the multivariable T(1) cancellation condition.
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