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• # Artykuł - szczegóły

## Studia Mathematica

2012 | 211 | 1 | 71-94

## Carleson measures associated with families of multilinear operators

EN

### Abstrakty

EN
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].

71-94

wydano
2012

### Twórcy

autor
• Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.
autor
• Departamento de Matemática, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91509-900, Brazil