Related papers: Weak Type Endpoint Estimates for the Commutators o…

The purpose of this article is to provide an alternative proof of the weak-type $\left(1,\ldots,1;\frac{1}{m}\right)$ estimate for $m$-multilinear Calder\'on-Zygmund operators on $\mathbb{R}^n$ first proved by Grafakos and Torres.…

Fix a bounded planar domain $\Omega.$ If an operator $T,$ in the Cowen-Douglas class $B_1(\Omega),$ admits the compact set $\bar{\Omega}$ as a spectral set, then the curvature inequality $\mathcal K_T(w) \leq - 4 \pi^2 S_\Omega(w,w)^2,$…

In this work we obtain weighted boundedness results for singular integral operators with kernels exhibiting exponential decay. We also show that the classes of weights are characterized by a suitable maximal operator. Additionally, we study…

In this paper, the boundedness properties of vector-valued intrinsic square functions and their vector-valued commutators with $BMO(\mathbb R^n)$ functions are discussed. We first show the weighted strong type and weak type estimates of…

We prove quantitative matrix weighted endpoint estimates for the matrix weighted Hardy-Littlewood maximal operator, Calder\'on-Zygmund operators, and commutators of CZOs with scalar BMO functions, when the matrix weight is in the class…

In this paper, we study representations of the vertex operator algebra $L(k,0)$ at one-third admissible levels $k= -5/3, -4/3, -2/3$ for the affine algebra of type $G_2^{(1)}$. We first determine singular vectors and then obtain a…

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 first consider two types of localizations of singular integral operators of convolution type, and show, under mild decay and smoothness conditions on the auxiliary functions, that their boundedness on the local Hardy space…

We study a family of convolution operators whose kernels have a singularity on the unit sphere. As a result, we prove the regarding L^p-L^q Sobolev inequalities.

In this paper, the author considers the weighted vector-valued estimate for the operator defined by $$T_Af(x)={\rm p.\,v.}\int_{\mathbb{R}^n}\frac{\Omega(x-y)}{|x-y|^{n+1}}\big(A(x)-A(y)-\nabla A(y)\big)f(y){\rm d}y,$$ and the corresponding…

We consider here one-parameter semigroups ${\bf T}=(T(t))_{t>0}$ of bounded operators on a Banach space $X$ which are weakly continuous in the sense of Arveson. For such a semigroup ${\bf T}$ denote by ${\mathcal M}_{\omega_{\bf T}}$ the…

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…

In this paper, we consider the degenerate and singular oscillatory integral operator with a singular kernel which is not a Calder\'{o}n-Zygmund kernel and satisfies suitable size and derivative conditions related to a real parameter $\mu$.…

We establish conditions in the spirit of the T1 theorem of David and Journ\'e which guarantee the boundedness of \nabla T on L^p(\R^n), where T is an integral transformation and 1<p<\infty. These are natural size and regularity conditions…

We prove weak-type (1,1) estimates for compositions of maximal operators with singular integrals. Our main object of interest is the operator $\Delta^*\Psi$ where $\Delta^*$ is Bourgain's maximal multiplier operator and $\Psi$ is the sum of…

We find a minimal notion of non-degeneracy for bilinear singular integral operators $T$ and identify testing conditions on the multiplying function $b$ that characterize the $L^p\times L^q\to L^r,$ $1<p,q<\infty$ and $r>\frac{1}{2},$…

Let A be a commutative ring, and let \a = \frak{a} be a finitely generated ideal in it. It is known that a necessary and sufficient condition for the derived \a-torsion and \a-adic completion functors to be nicely behaved is the weak…

In this paper we obtain the weak type (1,1) boundedness of Calderon-Zygmund operators acting over operator-valued functions. Our main tools for its solution are a noncommutative form of Calderon-Zygmund decomposition in conjunction with a…

We study the behaviour of sequences $U_2^n X U_1^{-n}$, where $U_1, U_2$ are unitary operators, whose spectral measures are singular with respect to the Lebesgue measure, and the commutator $XU_1-U_2X$ is small in a sense. The conjecture…

In this paper, we prove some BMO end-point estimates for some vector-valued multilinear operators related to certain singular integral operators.