Carleson measures associated with families of multilinear operators

Loukas Grafakos, and Lucas Oliveira. "Carleson measures associated with families of multilinear operators." Studia Mathematica 211.1 (2012): 71-94. <http://eudml.org/doc/285714>.

@article{LoukasGrafakos2012,
abstract = {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].},
author = {Loukas Grafakos, Lucas Oliveira},
journal = {Studia Mathematica},
keywords = {Carleson measure; multilinear operator},
language = {eng},
number = {1},
pages = {71-94},
title = {Carleson measures associated with families of multilinear operators},
url = {http://eudml.org/doc/285714},
volume = {211},
year = {2012},
}

TY - JOUR
AU - Loukas Grafakos
AU - Lucas Oliveira
TI - Carleson measures associated with families of multilinear operators
JO - Studia Mathematica
PY - 2012
VL - 211
IS - 1
SP - 71
EP - 94
AB - 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].
LA - eng
KW - Carleson measure; multilinear operator
UR - http://eudml.org/doc/285714
ER -