Weak and Strong Type Weighted Estimates for Multilinear Calderón-Zygmund Operators

Abstract

In this paper, we study the weighted estimates for multilinear Calderón-Zygmund operators %with multiple $A_{\vec{P}}$ weights from $L^{p_1}(w_1)\times ...\times L^{p_m}(w_m)$ to $L^p(v_{\vec{w}})$, where $1<p,p_1,...,p_m<\infty$ with $1/p_1+...+1/p_m=1/p$ and $\vec{w}=(w_1,...,w_m)$ is a multiple $A_{\vec{P}}$ weight. We give weak and strong type weighted estimates of mixed $A_p$-$A_{\infty }$ type. Moreover, the strong type weighted estimate is sharp whenever ${\max }_i{p}_i\le p^{\prime }/(mp-1)$.

References in corpus (2)

• Sharp weighted estimates for classical operators
• A characterization of two weight norm inequalities for maximal singular integrals with one doubling measure