Revista Matemática Iberoamericana


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Volume 31, Issue 2, 2015, pp. 609–616
DOI: 10.4171/RMI/847

Published online: 2015-07-16

Multilinear paraproducts revisited

Loukas Grafakos[1], Danqing He[2], Nigel Kalton[3] and Mieczysław Mastyło[4]

(1) University of Missouri, Columbia, USA
(2) University of Missouri, Columbia, USA
(3) University of Missouri, Columbia, USA
(4) Adam Mickiewicz University, Poznan, Poland

We prove that multilinear paraproducts are bounded from products of Lebesgue spaces $L^{p_1}\!\times \cdots \times L^{p_{m+1}}$ to $L^{p,\infty}$, when $1\le\! p_1, \dots , p_m$, $p_{m+1}<\infty$, $1/p_1+\cdots +1/p_{m+1}=1/p$. We focus on the endpoint case when some indices $p_j $ are equal to $1$, in particular we obtain a new proof of the estimate $L^1\times \cdots \times L^1\to L^{1/(m+1),\infty}$.

Keywords: Paraproducts, multilinear operators

Grafakos Loukas, He Danqing, Kalton Nigel, Mastyło Mieczysław: Multilinear paraproducts revisited. Rev. Mat. Iberoamericana 31 (2015), 609-616. doi: 10.4171/RMI/847