Carleson measures associated with families of multilinear operators

Loukas Grafakos; Lucas Oliveira

Studia Mathematica, Tome 209 (2012), p. 71-94 / Harvested from The Polish Digital Mathematics Library

Résumé

We investigate the construction of Carleson measures from families of multilinear integral operators applied to tuples of $L^{\infty}$ 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 $| R_{t} (b ₁, . . ., b ₘ) (x) | ² d x d t / t$ is Carleson. However, if the family of multilinear operators has cancellation in all variables combined, this result is still valid if $b_{j}$ are $L^{\infty}$ 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].

Publié le : 2012-01-01

Zbl 1267.42025

EUDML-ID : urn:eudml:doc:285714

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     title = {Carleson measures associated with families of multilinear operators},
     journal = {Studia Mathematica},
     volume = {209},
     year = {2012},
     pages = {71-94},
     zbl = {1267.42025},
     language = {en},
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Loukas Grafakos; Lucas Oliveira. Carleson measures associated with families of multilinear operators. Studia Mathematica, Tome 209 (2012) pp. 71-94. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm211-1-4/