arXiv subjects
Publications and source records attributed to Kangwei Li.
In this paper, we study the characterization of two weight inequality for multilinear fractional maximal operators. We give a multilinear analogue of Sawyer's two weight test condition.
We investigate the weighted bounds for multilinear maximal functions and Calderón-Zygmund operators from $L^{p_1}(w_1)\times...\times L^{p_m}(w_m)$ to $L^{p}(v_{\vec{w}})$, where $1<p_1,...,p_m<\infty$ with $1/{p_1}+...+1/{p_m}=1/p$ and $\vec{w}$ is a multiple $A_{\vec{P}}$ weight. We prove the sharp bound for the multilinear maximal function for all such $p_1,..., p_m$ and prove the sharp bound for $m$-linear Calderón-Zymund operators when $p\geq 1$.
In this paper, we introduce a class of singular integral operators which generalize Calderón-Zygmund operators to the more general case, where the set of singular points of the kernel need not to be the diagonal, but instead, it can be a general hyper curve. We show that such operators have similar properties as ordinary Calderón-Zygmund operators. In particular, we prove that they are of weak-type $(1, 1)$ and strong type $(p,p)$ for $1<p<\infty$.
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 $\max_i p_i \le p'/(mp-1)$.