Related papers: Regularizations of general singular integral opera…

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…

The aim of this paper is to get the boundedness of certain sublinear operators with rough kernel generated by Calder\'on-Zygmund operators on the generalized weighted Morrey spaces under generic size conditions which are satisfied by most…

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 investigate a class of Fourier integral operators with weakened symbols, which satisfy a multi-parameter differential inequality in $\R^n$. We establish that these operators retain the classical $L^p$ boundedness and the $H^1$ to $L^1$…

In this article, we begin a systematic study of the boundedness and the nuclearity properties of multilinear periodic pseudo-differential operators and multilinear discrete pseudo-differential operators on $L^p$-spaces. First, we prove…

We introduce and study in a general setting the concept of homogeneity of an operator and, in particular, the notion of homogeneity of an integral operator. In the latter case, homogeneous kernels of such operators are also studied. The…

In this paper we characterize BMO in terms of the boundedness of commutators of various bilinear singular integral operators with pointwise multiplication. In particular, we study commutators of a wide class of bilinear operators of…

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…

We prove boundedness results for integral operators of fractional type and their higher order commutators between weighted spaces, including $L^p$-$L^q$, $L^p$-$BMO$ and $L^p$-Lipschitz estimates. The kernels of such operators satisfy…

We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…

We present an intrinsically defined algebra of operators containing the right and left invariant Calder\'on-Zygmund operators on a stratified group. The operators in our algebra are pseudolocal and bounded on L^p (1<p<\infty). This algebra…

We study a class of oscillatory hypersingular integral operators associated to a radial hypersurface of the form $\Gamma(t)=(t,\varphi(t)), t\in\R{n}$. When $\varphi$ satisfies suitable curvature and monotonicity conditions, we prove…

We show that a positive operator between $L^p$-spaces is given by integration against a kernel function if and only if the image of each positive function has a lower semi-continuous representative with respect to a suitable topology. This…

The well-known curvature method initiated in works of Melnikov and Verdera is now commonly used to relate the $L^2(\mu)$-boundedness of certain singular integral operators to the geometric properties of the support of measure $\mu$, e.g.…

We study a family of fractional integral operators whose kernels satisfying an non-isotropic dilation have singularity on a coordinate subspace. A characterization is given for these operators bounded from the classical, atom decomposable…

Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations…

We establish $L^p$-boundedness for a class of operators that are given by convolution with product kernels adapted to curves in the space. The $L^p$ bounds follow from the decomposition of the adapted kernel into a sum of two kernels with…

We give a criterion for the global boundedness of integral operators which are known to be locally bounded. As an application, we discuss the global $L^p$-boundedness for a class of Fourier integral operators. While the local…

We study nonlocal convolution-type operators with singular, possibly anisotropic kernels. Our main objective is to establish and quantify their nonlocal-to-local convergence to a local differential operator with natural boundary conditions,…

We study the structure of strictly singular non-compact operators between $L_p$ spaces. Answering a question raised in [Adv. Math. 316 (2017), 667-690], it is shown that there exist operators $T$, for which the set of points…