Related papers: Causal sparse domination of Beurling maximal regul…

In this note we give simple proofs of several results involving maximal truncated Calde\'on-Zygmund operators in the general setting of rearrangement invariant quasi-Banach function spaces by sparse domination. Our techniques allow us to…

We prove that scalar-valued sparse domination of a multilinear operator implies vector-valued sparse domination for tuples of quasi-Banach function spaces, for which we introduce a multilinear analogue of the UMD condition. This condition…

We prove sharp weighted estimates for the non-tangential maximal function of singular integrals mapping functions from $\mathbf{R}^n$ to the half-space in $\mathbf{R}^{1+n}$ above $\mathbf{R}^n$. The proof is based on pointwise sparse…

In this paper we consider a generalized version of bounded oscillation operators, involving new parameters in the definition, as well as considering the operators on vector-valued function spaces. With this definition we will capture some…

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…

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…

The purpose of this paper is to study sparse domination estimates of composition operators in the setting of complex function theory. The method originates from proofs of the $A_2$ theorem for Calder\'on-Zygmund operators in harmonic…

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 general sparse domination theorem in a space of homogeneous type, in which a vector-valued operator is controlled pointwise by a positive, local expression called a sparse operator. We use the structure of the operator to get…

We introduce a class of operators on abstract measure spaces, which unifies the Calder\'on-Zygmund operators on spaces of homogeneous type, the maximal functions and the martingale transforms. We prove that such operators can be dominated…

In this paper, we study the behavior of the weighted composition operators acting on Bergman spaces defined on strictly pseudoconvex domains via the sparse domination technique from harmonic analysis. As a byproduct, we also prove a…

We prove $L^p(w)$ bounds for the Carleson operator ${\mathcal C}$, its lacunary version $\mathcal C_{lac}$, and its analogue for the Walsh series $\W$ in terms of the $A_q$ constants $[w]_{A_q}$ for $1\le q\le p$. In particular, we show…

We prove weighted weak-type $(r,r)$ estimates for operators satisfying $(r,s)$ limited-range sparse domination of $\ell^q$-type. Our results contain improvements for operators satisfying limited-range and square function sparse domination.…

Bounded Oscillation (BO) operators were recently introduced in the author's paper [13], where it was proved that many operators in harmonic analysis (Calder\'on-Zygmund operators, Carleson type operators, martingale transforms,…

Lebesgue space bounds $L^{p_1}({\mathbb R}^1) \times L^{p_2}(^1) \to L^q({\mathbb R}^1)$ are established for certain maximal bilinear operators. The proof combines a trilinear smoothing inequality with Calder\'on-Zygmund theory. A reference…

In this note, we show that if $T$ is a Calder\'on--Zygmund operator satisfying $T(1)=0$, then the usual sparse domination for $T$ can be sharpened by replacing local averages by local mean oscillations. As an application, we characterize…

Given sparse collections of measurable sets $\mathcal S_k$, $k=1,2,\ldots ,N$, in a general measure space $(X,\mathfrak M,\mu)$, let $ \Lambda_{\mathcal S_k}$ be the sparse operator, corresponding to $\mathcal S_k$. We show that the maximal…

We study discrete random variants of the Carleson maximal operator. Intriguingly, these questions remain subtle and difficult, even in this setting. Let $\{X_m\}$ be an independent sequence of $\{0,1\}$ random variables with expectations \[…

Let $K$ be a standard H\"older continuous Calder\'on--Zygmund kernel on $\mathbb{R}^{\mathbf{d}}$ whose truncations define $L^2$ bounded operators. We show that the maximal operator obtained by modulating $K$ by polynomial phases of a fixed…

In this paper we obtain quantitative weighted $L^p$-inequalities for some operators involving Bessel convolutions. We consider maximal operators, Littlewood-Paley functions and variational operators. We obtain $L^p(w)$-operator norms in…