Related papers: Convolution operators defined by singular measures…

Recent results of M.Junge and Q.Xu on the ergodic properties of the averages of kernels in noncommutative L^p-spaces are applied to the analysis of the almost uniform convergence of operators induced by the convolutions on compact quantum…

We prove $L^p$ boundedness results, $p > 2$, for local maximal averaging operators over a smooth 2D hypersurface $S$ with either a $C^1$ density function or a density function with a singularity that grows as $|(x,y)|^{-\beta}$ for $\beta <…

We consider singular integral operators and maximal singular integral operators with rough kernels on homogeneous groups. We prove certain estimates for the operators that imply $L^p$ boundedness of them by an extrapolation argument under a…

Using some resolution of singularities and oscillatory integral methods in conjunction with appropriate damping and interpolation techniques, L^p boundedness theorems for p > 2 are obtained for maximal operators over a wide range of…

We consider a class of operators defined by taking averages along polynomial sequences in discrete nilpotent groups. In this paper we prove $L^2$ boundedness of discrete singular Radon transforms along general polynomial sequences in…

We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type (1,1) inequalities. As an application, we prove that the best constants for…

To study operator algebras with symmetries in a wide sense we introduce a notion of {\em relative convolution operators} induced by a Lie algebra. Relative convolutions recover many important classes of operators, which have been already…

We prove that convolution with affine arclength measure on the curve parametrized by $h(t) := (t,t^2,...,t^n)$ is a bounded operator from $L^p(\mathbb{R}^n)$ to $L^q(\mathbb{R}^n)$ for the full conjectured range of exponents, improving on a…

A convolution operator in $\mathbb{R}^d$ with kernel in $L_q$ acts from $L_p$ to $L_s$, where $1/p+1/q=1+1/s$. The main theorem states that if $1<q,p,s<\infty$, then there exists an $L_p$ function of unit norm on which the $s$-norm of the…

We study a new class of pseudo differential operators whose symbols satisfy the differential inequality with a mixture of homogeneities. On the other hand, by taking singular integral realization, it can be equivalently defined by kernels…

Let $\mathbb{H}^{n}$ be the Heisenberg group. For $0 \leq \alpha < Q=2n+2$ and $N \in \mathbb{N}$ we consider exponent functions $p(\cdot) : \mathbb{H}^{n} \to (0, +\infty)$, which satisfies H\"older conditions, such that $\frac{Q}{Q+N} <…

We explore boundedness properties in the context of metric measure spaces, of some natural operators of convolution type whose study is suggested by certain transformations used in computer vision.

In the present paper we characterize the existence and uniqueness of maximal Lp-regular solutions of high order convolution operator equations. Particularly, we get coercive uniform estimates with respect to spectral parameter and we show…

We introduce the notion of a family of convolution operators associated with a given elliptic partial differential operator. Such a convolution structure is shown to exist for a general class of Laplace-Beltrami operators on two-dimensional…

Let $K$ be a field of characteristic zero, $X$ and $Y$ be smooth $K$-varieties, and let $G$ be a algebraic $K$-group. Given two algebraic morphisms $\varphi:X\rightarrow G$ and $\psi:Y\rightarrow G$, we define their convolution…

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…

In this paper we establish that several maximal operators of convolution type, associated to elliptic and parabolic equations, are variation-diminishing. Our study considers maximal operators on the Euclidean space $\mathbb{R}^d$, on the…

In the first part, we obtain sharp results for L^2 boundedness of strongly singular operators on the Heisenberg group. We also define the oscillating convolution operators on the Heisenberg group and study their boundedness properties. In…

Let $\sigma=(\sigma_{1},\sigma_{2},\dots,\sigma_{n})\in \mathbb{S}^{n-1}$ and $d\sigma$ denote the normalised Lebesgue measure on $\mathbb{S}^{n-1},~n\geq 2$. For functions $f_1, f_2,\dots,f_n$ defined on $\R$ consider the multilinear…

We study Lp-improving properties as well as the type set of certain singular measures on the Heisenberg group.