Related papers: Convex body domination and weighted estimates with…

In this paper, the author considers the weighted vector-valued estimate for the operator defined by $$T_Af(x)={\rm p.\,v.}\int_{\mathbb{R}^n}\frac{\Omega(x-y)}{|x-y|^{n+1}}\big(A(x)-A(y)-\nabla A(y)\big)f(y){\rm d}y,$$ and the corresponding…

We prove that the operator norm on weighted Lebesgue space L2(w) of the commutators of the Hilbert, Riesz and Beurling transforms with a BMO function b depends quadratically on the A2-characteristic of the weight, as opposed to the linear…

Let $X$ be a space of homogeneous type and let $L$ be a sectorial operator with bounded holomorphic functional calculus on $L^2(X)$. We assume that the semigroup $\{e^{-tL}\}_{t>0}$ satisfies Davies-Gaffney estimates. In this paper, we…

In this paper we provide some quantitative mixed-type estimates assuming conditions that imply that $uv\in A_{\infty}$ for Calder\'on-Zygmund operators, rough singular integrals and commutators. The main novelty of this paper lies in the…

In this work we fully characterize the classes of matrix weights for which multilinear Calder\'on-Zygmund operators extend to bounded operators on matrix weighted Lebesgue spaces. To this end, we develop the theory of multilinear singular…

We obtain Musielak Orlicz bumps conditions on a pair of weights for the boundedness of Calder\'on Zygmund operators and their commutators between variable Lebesgue spaces with different weights. The symbols of the commutators belong to a…

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calder\'on--Zygmund type operators $T_\theta$ in these new weighted spaces. Furthermore, the…

Calder\'on-Zygmund operators with noncommuting kernels may fail to be Lp-bounded for $p \neq 2$, even for kernels with good size and smoothness properties. Matrix-valued paraproducts, Fourier multipliers on group vNa's or noncommutative…

In this paper we consider bilinear sparse forms intimately related to iterated commutators of a rather general class of operators. We establish Bloom weighted estimates for these forms in the full range of exponents, both in the diagonal…

We establish the characterization of compactness for the sparse operator (associated with symbol in weighted VMO space) in the two weight setting on the spaces of homogeneous type in the sense of Coifman and Weiss. As a direct application…

This paper refines the main results from our previous study on sparse bounds of generalized commutators of multilinear fractional singular integral operators in \cite{CenSong2412}. The key improvements are: 1. We replace pointwise…

We prove Bloom type two-weight inequalities for commutators of multilinear singular integral operators including Calder\'on-Zygmund operators and their dyadic counterparts. Such estimates are further extended to a general higher order…

We prove boundedness of Calder\'on-Zygmund operators acting in Banach functions spaces on domains, defined by the $L_1$ Carleson functional and $L_q$ ($1<q<\infty$) Whitney averages. For such bounds to hold, we assume that the operator maps…

We study the domination of the lattice Hardy--Littlewood maximal operator by sparse operators in the setting of general Banach lattices. We prove that the admissible exponents of the dominating sparse operator are determined by the…

The recent proof of the sharp weighted bound for Calder\'on-Zygmund operators has led to much investigation in sharp mixed bounds for operators and commutators, that is, a sharp weighted bound that is a product of at least two different…

We consider $\ell^r$ extensions of Calderon-Zygmund operators on weighted spaces $L^p(w)$ with $w$ an $A_p$ weight and $1 < p < \infty$. We give quantitative estimates of these operators' norm in terms of a given weight's $A_p$…

We complete our theory of weighted $L^p(w_1) \times L^q(w_2) \to L^r(w_1^{r/p} w_2^{r/q})$ estimates for bilinear bi-parameter Calder\'on--Zygmund operators under the assumption that $w_1 \in A_p$ and $w_2 \in A_q$ are bi-parameter weights.…

We consider maximal operators acting on vector valued functions, that is, functions taking values on $\mathbb{C}^d,$ that incorporate matrix weights in their definitions. We show vector valued estimates, in the sense of Fefferman--Stein…

We study sparse domination for operators defined with respect to an atomic filtration on a space equipped with a general measure $\mu$. In the case of Haar shifts, $L^p$-boundedness is known to require a weak regularity condition, which we…

In this paper, we give necessary and sufficient conditions for weighted $L^2$ estimates with matrix-valued measures of well localized operators. Namely, we seek estimates of the form: \[ \| T(\mathbf{W} f)\|_{L^2(\mathbf{V})} \le…