Weak and Strong Type Weighted Estimates for Multilinear Calder\'{o}n-Zygmund Operators

In this paper, we study the weighted estimates for multilinear Calder\'{o}n-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 $\max_i p_i \le p'/(mp-1)$

Weak and strong ApA_p-A∞A_\infty estimates for square functions and related operators

We prove sharp weak and strong type weighted estimates for a class of dyadic operators that includes majorants of both standard singular integrals and square functions. Our main new result is the optimal bound $[w]_{A_p}^{1/p}[w]_{A_\infty}^{1/2-1/p}\lesssim [w]_{A_p}^{1/2}$ for the weak type norm of square functions on $L^p(w)$ for $p>2$; previously, such a bound was only known with a logarithmic correction. By the same approach, we also recover several related results in a streamlined manner.Comment: 12 pages, typos corrected. Accepted for publication in Proc. Amer. Math. So

New bounds for bilinear Calder\'on-Zygmund operators and applications

In this work we extend Lacey's domination theorem to prove the pointwise control of bilinear Calder\'on--Zygmund operators with Dini--continuous kernel by sparse operators. The precise bounds are carefully tracked following the spirit in a recent work of Hyt\"onen, Roncal and Tapiola. We also derive new mixed weighted estimates for a general class of bilinear dyadic positive operators using multiple $A_{\infty}$ constants inspired in the Fujii-Wilson and Hrus\v{c}\v{e}v classical constants. These estimates have many new applications including mixed bounds for multilinear Calder\'on--Zygmund operators and their commutators with $BMO$ functions, square functions and multilinear Fourier multipliers.Comment: 35 pages, accepted for publication in Revista Matem\'atica Iberoamerican