Carleson measures associated with families of multilinear operators

• Autorzy: Loukas Grafakos , Lucas Oliveira
• Języki publikacji: 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].

Kategorie tematyczne

• 42B99: None of the above, but in this section
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 211
• Numer: 1
• Strony: 71-94

Daty

wydano

2012

Twórcy

autor

Loukas Grafakos

• Department of Mathematics, University of Missouri, Columbia, MO 65211, U.S.A.

autor

Lucas Oliveira

• Departamento de Matemática, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91509-900, Brazil

Identyfikatory

DOI

10.4064/sm211-1-4