Related papers: Weak type bounds for rough maximal singular integr…

Let $\mathcal{B}$ denote a nonempty translation invariant collection of intervals in $\mathbb{R}^n$ (which we regard as a rare basis), and define the associated geometric maximal operator $M_\mathcal{B}$ by $$M_\mathcal{B}f(x) = \sup_{x \in…

Let $g$ be an analytic function on the unit disc and consider the integration operator of the form $T_g f(z) = \int_0^z fg'\,d\zeta$. We show that on the spaces $H^1$ and $BMOA$ the operator $T_g$ is weakly compact if and only if it is…

In this paper we obtain for $T^+$, a one-sided singular integral given by a Calder\'on-Zygmund kernel with support in $(-\infty,0)$, a $L^p(w)$ bound when $w\in A_1^+$. A. K. Lerner, S. Ombrosi, and C. P\'erez proved in [ "$A_{1}$ Bounds…

In this paper, we systematically study weighted jump and variational inequalities for rough operators. More precisely, we show some weighted jump and variational inequalities for the families $\mathcal T:=\{T_\varepsilon\}_{\varepsilon>0}$…

In this work, we establish $L^{p_1}\times \cdots\times L^{p_m}\to L^p$ bounds for maximal multi-(sub)linear singular integrals associated with homogeneous kernels $\frac{\Omega(\vec{\boldsymbol{y}}')}{|\vec{\boldsymbol{y}}|^{mn}}$ where…

In this paper, we will give the weighted bounds for multilinear fractional maximal type operators $\mathcal{M}_{\Omega,\alpha}$ with rough homogeneous kernels. We obtain a mixed $A_{(\vec{P},q)}-A_\infty$ bound and a $A_{\vec{P}}$ type…

We prove that in any metric space $(X,d)$ the singular integral operators {equation*} T^k_{\mu,\ve}(f)(x)=\int_{X\setminus B(x,\varepsilon)}k(x,y)f(y)d\mu (y).{equation*} converge weakly in some dense subspaces of $L^2(\mu)$ under minimal…

Let $K$ be the Calder\'on-Zygmund convolution kernel on $\mathbb{R}^d (d\geq2)$. Define the commutator associated with $K$ and $a\in L^\infty(\mathbb{R}^d)$ by \[ T_af(x)=p.v. \int K(x-y)m_{x,y}a\cdot f(y)dy. \] Recently, Grafakos and…

In this paper, we study the quantitative weighted bounds for the $q$-variational singular integral operators with rough kernels. The main result is for the sharp truncated singular integrals itself $$…

In this article, we prove weak type $(1,1)$ bounds for the variation and jump operators corresponding to the family of truncations of singular integrals with rough kernels. This resolves an open question raised by Jones, Seeger and Wright…

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 study the rough bilinear singular integral, introduced by Coifman and Meyer , $$ T_\Omega(f,g)(x)=p.v. \! \int_{\mathbb R^{n}}\! \int_{\mathbb R^{n}}\! |(y,z)|^{-2n} \Omega((y,z)/|(y,z)|)f(x-y)g(x-z) dydz, $$ when $\Omega $ is a function…

This paper is devoted to the study of noncommutative maximal operators with rough kernels. More precisely, we prove the weak type $(1,1)$ boundedness for noncommutative maximal operators with rough kernels. The proof of weak type (1,1)…

A weak type $(1,1)$ estimate is established for the first order $d$-commutator introduced by Christ and Journ\'e, in dimension $d\ge 2$.

Convolution type Calder\'on-Zygmund singular integral operators with rough kernels $\pv \Om(x)/|x|^n$ are studied. A condition on $\Om$ implying that the corresponding singular integrals and maximal singular integrals map $L^p \to L^p$ for…

We consider weighted $L^p(w)$ boundedness ($1<p<\infty $ and $w$ a Muckenhoupt $A_p$ weight) of the Calder\'{o}n commutator $\mathcal C_\Omega$ associated with rough homogeneous kernel, under the condition $\Omega\in L^q(\mathbb S^{n-1})$…

We prove quantitative, one-weight, weak-type estimates for maximal operators, singular integrals, fractional maximal operators and fractional integral operators. We consider a kind of weak-type inequality that was first studied by…

The operators $\Lambda_m$ ($m\in\mathbb{N}\cup \{0\}$) arise when one studies the action of the Beurling-Ahlfors transform on certain radial function subspaces. It is known that the weak-type $(1,1)$ constant of $\Lambda_0$ is equal to…

In this paper, we investigate the boundedness of bilinear Calder\'on-Zygmund operators $T$ from ${L^{p_1}\left(w_1\right)} \times {L^{p_2}\left(w_2\right)}$ to ${L^{p,\infty}\left(v_{\vec{w}}\right)}$ with the stopping time method, where $1…

We study weighted norm inequalities of $(1,q)$- type for $0<q<1$, $\Vert \mathbf{G} \nu \Vert_{L^q(\Omega, d \sigma)} \le C \, \Vert \nu \Vert, \quad \text{for all positive measures $\nu$ in $\Omega$},$ along with their weak-type…