Related papers: Sparse dominations and weighted variation inequali…
In this note, we show that if $T$ is a multilinear singular integral operator associated with a kernel satisfies the so-called multilinear $L^{r}$-H\"ormander condition, then $T$ can be dominated by multilinear sparse operators.
In this paper we obtain a pointwise sparse domination for generalized H\"ormander operators and also for iterated commutators with those operators. As a particular case of our result we obtain a extension of the sparse domination for…
In this paper, we establish quantitative weak type estimates for operators that are dominated by (fractional) sparse operators in bilinear sense. Specifically, we derive bounds for both the restricted weak type $L^{p,1}\rightarrow…
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…
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 paper we study the commutators of fractional type integral operators. This operators are given by kernels of theform $$K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),$$ where $A_i$ are invertibles matrices and each $k_i$ satisfies a…
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…
We consider operators $T$ satisfying a sparse domination property \[ |\langle Tf,g\rangle|\leq c\sum_{Q\in\mathscr{S}}\langle f\rangle_{p_0,Q}\langle g\rangle_{q_0',Q}|Q| \] with averaging exponents $1\leq p_0<q_0\leq\infty$. We prove…
In this paper, we prove bilinear sparse domination bounds for a wide class of Fourier integral operators of general rank, as well as oscillatory integral operators associated to H\"ormander symbol classes $S^m_{\rho,\delta}$ for all…
In this work, by recent work of Lerner and Ombrasi (J. Geom. Anal. 30(1): 1011-1027, 2020), we show a maximally modulated singular integral operator which its kernel satisfying $L^r$- H\"ormander condition can be dominated by sparse…
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…
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 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…
Let $\Omega$ be homogeneous of degree zero and have mean value zero on the unit sphere ${S}^{n-1}$, $T_{\Omega}$ be the convolution singular integral operator with kernel $\frac{\Omega(x)}{|x|^n}$. For $b\in{\rm BMO}(\mathbb{R}^n)$, let…
We establish analogs of sharp weighted weak-type bounds for $m$-sublinear operators satisfying sparse form domination, including multilinear Calder\'on-Zygmund singular integrals. Our results, which hold for general $\vec{p} \in…
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…
We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of weighted estimates…
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.…
In this paper, we systematically study the Fefferman-Stein inequality and Coifman-Fefferman inequality for the general commutators of singular integral operators that satisfy H\"{o}rmander conditions of Young type. Specifically, we first…
In this paper we study Coifman type estimates and weighted norm inequalities for singular integral operators $T$ and its commutators, given by the convolution with a vector valued kernel $K$. We define a weaker H\"ormander type condition…