Related papers: A T1 theorem for weakly singular integral operator…

The natural BMO (bounded mean oscillation) conditions suggested by scalar-valued results are known to be insufficient for the boundedness of operator-valued paraproducts. Accordingly, the boundedness of operator-valued singular integrals…

We prove a Tb Theorem that characterizes all Calderon-Zygmund operators that extend compactly on L^p(R^n), 1<p<\infty . The result, whose proof does not require the property of accretivity, can be used to prove compactness of the Double…

Recently, V. Cruz, J. Mateu and J. Orobitg have proved a T(1) theorem for the Beurling transform in the complex plane. It asserts that given $0<s\leq1$, $1<p<\infty$ with $sp>2$ and a Lipschitz domain $\Omega\subset \mathbb{C}$, the…

Given a Lipschitz domain $D\subset \mathbb{R}^d,$ a Calder\'on-Zygmund operator $T$ and a modulus of continuity $\omega(x),$ we solve a problem when the restricted operator $T_Df=T(f\chi_D)\chi_D$ sends the Campanato space…

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…

Given a real-analytic function b(x) defined on a neighborhood of the origin with b(0) = 0, we consider local convolutions with kernels which are bounded by |b(x)|^(-a), where a > 0 is the smallest number for which |b(x)|^(-a) is not…

Let $\mu$ be an $n$-dimensional finite positive measure on $\mathbb{R}^m$. We obtain a $T1$ condition sufficient for the boundedness of Calder\'{o}n-Zygmund operators on $\textrm{RBMO}(\mu)$, the regular BMO space of Tolsa.

We consider parabolic operators of the form $$\partial_t+\mathcal{L},\ \mathcal{L}:=-\mbox{div}\, A(X,t)\nabla,$$ in $\mathbb R_+^{n+2}:=\{(X,t)=(x,x_{n+1},t)\in \mathbb R^{n}\times \mathbb R\times \mathbb R:\ x_{n+1}>0\}$, $n\geq 1$. We…

In this manuscript we provide necessary and sufficient conditions for the $\textnormal{weak}(1,p)$ boundedness, $1< p<\infty,$ of discrete Fourier multipliers (Fourier multipliers on $\mathbb{Z}^n$). Our main goal is to apply the results…

In this article we give a molecular reconstruction theorem for $H_{\omega}^{p(\cdot)}(\mathbb{R}^{n})$. As an application of this result and the atomic decomposition developed in [5] we show that classical singular integrals can be extended…

Supplying the missing necessary conditions, we complete the characterisation of the $L^p\to L^q$ boundedness of commutators $[b,T]$ of pointwise multiplication and Calder\'on-Zygmund operators, for arbitrary pairs of $1<p,q<\infty$ and…

In this paper, we study the boundedness theory for maximal Calder\'on-Zygmund operators acting on noncommutative $L_p$-spaces. Our first result is a criterion for the weak type $(1,1)$ estimate of noncommutative maximal Calder\'on-Zygmund…

In this paper, by using the decomposition theorem for weak Hardy spaces, we will obtain the boundedness properties of some integral operators with variable kernels on these spaces, under some Dini type conditions imposed on the variable…

In the setting of spaces of homogeneous type, we give a direct proof of the local Tb theorem for singular integral operators. Motivated by questions of S. Hofmann, we extend it to the case when the integrability conditions are lower than 2,…

We prove the boundedness on $L^p$, $1<p<\infty$, of operators on manifolds which arise by taking conditional expectation of transformations of stochastic integrals. These operators include various classical operators such as second order…

Let $\Omega$ be homogeneous of degree zero, have vanishing moment of order one on the unit sphere $\mathbb {S}^{d-1}$($d\ge 2$). In this paper, our object of investigation is the following rough non-standard singular integral operator…

Nagel and Stein established $L^p$-boundedness for a class of singular integrals of NIS type, that is, non-isotropic smoothing operators of order 0, on spaces $\widetilde{M}=M_1\times...\times M_n,$ where each factor space $M_i, 1\leq i\leq…

Let $E \subset \mathbb{C}$ be a Borel set such that $0<\mathcal{H}^1(E)<\infty$. David and L\'eger proved that the Cauchy kernel $1/z$ (and even its coordinate parts $\textrm{Re}\, z/|z|^2$ and $\textrm{Im}\, z/|z|^2$, $z\in…

Let $T$ be an $L^2$-bounded operator having an $\omega$-Calder\'on--Zygmund kernel $K$ with a modulus of continuity $\omega$. If $\omega$ satisfied the Dini condition $\int_0^1\omega(t)\ud t/t<\infty$, then $T$ satisfies the $A_2$ theorem…

In this paper, we study the $L^{p}$ boundedness and $L^{p}(w)$ boundedness ($1<p<\infty$ and $w$ a Muckenhoupt $A_{p}$ weight) of fractional maximal singular integral operators $T_{\Omega,\alpha}^{\#}$ with homogeneous convolution kernel…