Related papers: Boundedness results for commutators with BMO funct…
In this paper, we consider the boundedness properties of multilinear $\theta$-type Calder\'on--Zygmund operators $T_\theta$ recently introduced in the literature. First, we prove strong type and weak type estimates for multilinear…
We give direct and inverse theorems for the weighted approximation of functions with endpoint singularities by combinations of Bernstein operators.
Multivariate sign functions are often used for robust estimation and inference. We propose using data dependent weights in association with such functions. The proposed weighted sign functions retain desirable robustness properties, while…
In this paper we provide quantitative Bloom type estimates for iterated commutators of fractional integrals improving and extending results from a work of Holmes, Rahm and Spencer. We give new proofs for those inequalities relying upon a…
In this article, we study the commutators of Hausdor? operator and establish their boundedness on weighted Herz space in the setting of Heisenberg group.
We prove new sufficient bump conditions for general iterated commutators of Calder\'on-Zygmund operators and fractional integral operators. As an application of our results we derive two weight compactness theorems for higher order iterated…
In a previous paper by one of us, a "compact version" of Rubio de Francia's weighted extrapolation theorem was proved, which allows one to extrapolate the compactness of an operator from just one space to the full range of weighted spaces,…
Let $L$ be the infinitesimal generator of an analytic semigroup on $L^2(\mathbb{R}^n)$ with Gaussian kernel bounds, and let $L^{-\alpha/2}$ be the fractional integrals of $L$ for $0<\alpha<n$. Assume that $\vec{b}=(b_1,b_2,\cdots,b_m)$ is a…
We provide a unified approach to MM-estimation with auxiliary scale for balanced linear models with structured covariance matrices. This approach leads to estimators that are highly robust against outliers and highly efficient for normal…
In this paper, we investigate the multilinear boundedness properties of the higher ($n$-th) order Calder\'on commutator for dimensions larger than two. We establish all multilinear endpoint estimates for the target space…
In this paper we investigate weighted norm inequalities for the commutator of a fractional integral operator and multiplication by a function. In particular, we show that, for $\mu,\lambda\in A_{p,q}$ and $\alpha/n+1/q=1/p$, the norm $\|…
In this paper, the authors first consider the bidirectional estimates of several typical integrals. As some applications of these integral estimates, the authors investigate the pointwise multipliers from the normal weight general function…
M-estmators including the Welsch and Cauchy have been widely adopted for robustness against outliers, but they also down-weigh the uncontaminated data. To address this issue, we devise a framework to generate a class of nonconvex functions…
In this work, we establish continuity properties of strongly singular integral operators for extreme values of $p$. Particularly, weighted $L^\infty$-$BMO$ boundedness is obtained, generalizing Miyachi's result to the context of Muckenhoupt…
In this paper we develop the method of finding sharp estimates by using a Bellman function. In such a form the method appears in the proofs of the classical John--Nirenberg inequality and $L^p$ estimations of BMO functions. In the present…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
We shall investigate the boundedness of the intrinsic square functions and their commutators on generalized weighted Orlicz-Morrey spaces $M^{\Phi,\varphi}_{w}({\mathbb R}^n)$. In all the cases, the conditions for the boundedness are given…
The so-called weighted solid Cauchy transform, from inside the unit disc into the complement of its closure, is considered and their basic properties such as boundedness is studied for appropriate probability measures. The action the disc…
Let $({\mathcal X},d,\mu)$ be a metric measure space satisfying both the upper doubling and the geometrically doubling conditions. In this paper, the authors establish some equivalent characterizations for the boundedness of fractional…
We provide convex body domination results for the generalized vector-valued commutator of those operators that admit specific forms of convex body domination themselves. We also prove some strong type estimates and other consequences of…