Weighted vector-valued bounds for a class of multilinear singular integral operators

Abstract

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};{\mathbb{R}}^n,w_1)\times \cdots \times L^{p_m}(l^{q_m};{\mathbb{R}}^n,w_m)$ to $L^p(l^q;{\mathbb{R}}^n,{\nu }_{\vec{w}})$, with $p_1,\dots ,p_m\in (1,\infty )$ and $1/p=1/p_1+\cdots +1/p_m$ and $\vec{w}$ is a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators.

22 pages, major revisionos of the last version: corrected misprints, an application to the commutator of Calderón is given

References in corpus (1)

• Weighted bounds for multilinear operators with non-smooth kernels