Related papers: Bounds for Calder\'on-Zygmund operators with matri…

For a matrix A_2 weight W on R^p, we introduce a new notion of W-Calder\'on-Zygmund matrix kernels, following earlier work in by Isralowitz. We state and prove a T1 theorem for such operators and give a representation theorem in terms of…

For an L ^2-bounded Calderon-Zygmund Operator T, and a weight w \in A_2, the norm of T on L ^2 (w) is dominated by A_2 characteristic of the weight. The recent theorem completes a line of investigation initiated by Hunt-Muckenhoupt-Wheeden…

We prove that for a Calderon-Zygmund operator and weight w\in A_2, that it satisfies the linear in A2 bound due to Hytonen. Our proof will appeal to a distributional inequality used by several authors, adapted Haar functions, and standard…

We give a self-contained proof of the $A_2$ conjecture, which claims that the norm of any Calderon-Zygmund operator is bounded by the first degree of the $A_2$ norm of the weight. The original proof of this result by the first author relied…

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 verify the $L^2$-boundedness for the jump functions and variations of Calder\'on-Zygmund singular integral operators with the underlying kernels satisfying \begin{align*}\int_{\varepsilon\leq |x-y|\leq N}…

It is well-known that several classical results about Calder\'{o}n-Zygmund singular integral operators can be extended to \(X\)-valued functions if and only if the Banach space \(X\) has the UMD property. The dependence of the norm of an…

Let $B$ be a locally integrable matrix function, $W$ a matrix A${}_p$ weight with $1 < p < \infty$, and $T$ be any of the Riesz transforms. We will characterize the boundedness of the commutator $[T, B]$ on $L^p(W)$ in terms of the…

We consider here a problem of finding the sharp estimate for the boundedness of an arbitrary Calder\'on-Zygmund operator in $L^2(w)$, $w\in A_2$. We first prove that for $A_2$ weight $w$ one has that the norm a Calderon--Zygmund operator…

We present a proof of the one-sided $A_2$ theorem in dimension one, with a logarithmic loss. This theorem concerns one-sided Calder\'on-Zygmund operators (CZOs) whose kernels $K(x,y)$ vanish whenever $x < y$. These operators are bounded on…

We use the Bellman function method to give an elementary proof of a sharp weighted estimate for the Haar shifts, which is linear in the $A_2$ norm of the weight and in the complexity of the shift. Together with the representation of a…

Let $p\in(1,\infty)$, $\rho\in (2, \infty)$ and $W$ be a matrix $A_p$ weight. In this article, we introduce a version of variation $\mathcal{V}_{\rho}({\mathcal T_n}_{\,,\,\ast})$ for matrix Calder\'on--Zygmund operators with modulus of…

We introduce the so called convex body valued sparse operators, which generalize the notion of sparse operators to the case of spaces of vector valued functions. We prove that Calder\'on--Zygmund operators as well as Haar shifts and…

We discuss weighted estimates for the squares of the Riesz transforms, R^{2}, on L^{2}(W) where W is a matrix A2 weight. We prove that if W is close to the Identity matrix Id, then the operator norm of R^{2} is close to its unweighted norm…

In this paper, we study the dyadic Carleson Embedding Theorem in the matrix weighted setting. We provide two new proofs of this theorem, which highlight connections between the matrix Carleson Embedding Theorem and both maximal functions…

For a general Calderon-Zygmund operator $T$ on $R^N$, it is shown that $\|Tf\|_{L^2(w)}\leq C(T)\|w\|_{A_2}\|f\|_{L^2(w)}$ for all Muckenhoupt weights $w\in A_2$. This optimal estimate was known as the $A_2$ conjecture. A recent result of…

Let $W$ denote a matrix $A_2$ weight. In this paper, we implement a scalar argument using the square function to deduce square-function type results for vector-valued functions in $L^2(\mathbb{R},\mathbb{C}^d)$. These results are then used…

We prove that the operator norm of every Banach space valued Calderon-Zygmund operator T on the weighted Lebesgue-Bochner space depends linearly on the Muckenhoupt A_2 characteristic of the weight. In parallel with the proof of the…

We give an overview of the generalized Calder\'on-Zygmund theory for "non-integral" singular operators, that is, operators without kernels bounds but appropriate off-diagonal estimates. This theory is powerful enough to obtain weighted…

This article develops a novel approach to the representation of singular integral operators of Calder\'on-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is…