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Corrigendum to "Carleson measures associated with families of multilinear operators" (Studia Math. 211 (2012), 71-94)

100%

Grafakos L., Oliveira L.

Studia Mathematica

2014

tom 221

nr 2

193-196

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.

Carleson measures associated with families of multilinear operators

100%

Grafakos L., Oliveira L.

Studia Mathematica

2012

tom 211

nr 1

71-94

We investigate the construction of Carleson measures from families of multilinear integral operators applied to tuples of $L^{∞}$ and BMO functions. We show that if the family $R_{t}$ of multilinear operators has cancellation in each variable, then for BMO functions b₁, ..., bₘ, the measure $|R_{t}(b₁, ..., bₘ)(x)|² dxdt/t$ is Carleson. However, if the family of multilinear operators has cancellation in all variables combined, this result is still valid if $b_{j}$ are $L^{∞}$ functions, but it may fail if $b_{j}$ are unbounded BMO functions, as we indicate via an example. As an application of our results we obtain a multilinear quadratic T(1) type theorem and a multilinear version of a quadratic T(b) theorem analogous to those by Semmes [Proc. Amer. Math. Soc. 110 (1990), 721-726].

Ograniczanie wyników

2 Studia Mathematica

2 Grafakos L.

2 Oliveira L.

1 2014

1 2012

Wyniki wyszukiwania

Corrigendum to "Carleson measures associated with families of multilinear operators" (Studia Math. 211 (2012), 71-94)

Carleson measures associated with families of multilinear operators