Related papers: On pointwise estimates involving sparse operators

We give a short proof of the sharp weighted bound for sparse operators that holds for all $p$, $1<p<\infty$. By recent developments this implies the bounds hold for any Calder\'on-Zygmund operator. The novelty of our approach is that we…

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…

This paper gives the pointwise sparse dominations for variation operators of singular integrals and commutators with kernels satisfying the $L^r$-H\"{o}rmander conditions. As applications, we obtain the strong type quantitative weighted…

We provide a versatile formulation of Lacey's recent sparse pointwise domination technique with a local weak type estimate on a nontangential maximal function as the only hypothesis. We verify this hypothesis for sharp variational…

In this paper, we establish sparse dominations for the Dunkl-Calder\'on-Zygmund operators and their commutators in the Dunkl setting. As applications, we first define the Dunkl-Muckenhoupt $A_p$ weight and obtain the weighted bounds for the…

We extend Lerner's recent approach to sparse domination of Calder\'on--Zygmund operators to upper doubling (but not necessarily doubling), geometrically doubling metric measure spaces. Our domination theorem is different from the one…

Pointwise estimates for the gradient of solutions to the $p$-Laplace system with right-hand side in divergence form are established. They enable us to develop a nonlinear counterpart of the classical Calder\'on-Zygmund theory in terms of…

We impose standard $ T1 $-type assumptions on a Calder\'on-Zygmund operator $ T $, and deduce that for bounded compactly supported functions $ f, g $ there is a sparse bilinear form $ \Lambda $ so that $$ \lvert \langle T f, g \rangle\rvert…

We present a new proof of the classical weak-type $(1,1)$ estimate for Calder\'on-Zygmund operators. This proof is inspired by ideas of Nazarov, Treil, and Volberg that address the non-doubling setting. An application to a weighted…

We prove that a large class of operators, which arise as the projections of martingale transforms of stochastic integrals with respect to Brownian motion, as well as other closely related operators, are in fact Calder\'on--Zygmund…

We prove weighted estimates for rough bilinear singular integral operators with kernel $$K(y_1, y_2) = \frac{\Omega((y_1,y_2)/|(y_1,y_2)|)}{|(y_1, y_2)|^{2d}},$$ where $y_i \in \mathbb{R}^{d}$ and $\Omega \in L^{\infty}(S^{2d-1})$ with…

We prove a bilinear form sparse domination theorem that applies to many multi-scale operators beyond Calder\'on-Zygmund theory, and also establish necessary conditions. Among the applications, we cover large classes of Fourier multipliers,…

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…

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…

By means of appropriate sparse bounds, we deduce compactness on weighted $L^p(w)$ spaces, $1<p<\infty$, for all Calder\'on-Zygmund operators having compact extensions on $L^2(\mathbb{R}^n)$. Similar methods lead to new results on…

We prove a pointwise estimate for positive dyadic shifts of complexity $m$ which is linear in the complexity. This can be used to give a pointwise estimate for Calder\'on-Zygmund operators and to answer a question posed by A. Lerner.…

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…

We represent a general bilinear Calder\'on-Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so called sparse T1…

For a limited range of indices $p$, we obtain $L^p(\mathbb{R}^n)$ boundedness for singular integral operators whose kernels satisfy a condition weaker than the typical H\"ormander smoothness estimate. These operators are assumed to be…

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…