On the approximation by convolution type double singular integral operators

Convolution operators defined by singular measures on the motion group

This paper contains an $L^{p}$ improving result for convolution operators defined by singular measures associated to hypersurfaces on the motion group. This needs only mild geometric properties of the surfaces, and it extends earlier results on Radon type transforms on $\mathbb{R}^{n}$. The proof relies on the harmonic analysis on the motion group.

乘积空间上非卷积类型的奇异积分

Singular integrals of non-convolution type on product spaces

研究乘积空间上符号满足混合齐性微分不等式的新型伪微分算子，证明其在 L^p 空间有界且构成代数。

Björk-Sjölin condition for strongly singular convolution operators on graded Lie groups

In this work we extend the $L^1$-Björk-Sjölin theory of strongly singular convolution operators to arbitrary graded Lie groups. Our criteria are presented in terms of the oscillating Hörmander condition due to Björk and Sjölin of the kernel of the operator, and the decay of its group Fourier transform is measured in terms of the infinitesimal representation of an arbitrary Rockland operator. The historical result by Björk and Sjölin is re-obtained in the case of the Euclidean space.

非局部到局部 $L^p$-收敛性：具有奇异各向异性核的卷积算子

Nonlocal-to-local $L^p$-convergence of convolution operators with singular, anisotropic kernels

本文研究了具有奇异各向异性核的非局部卷积算子向局部微分算子的非局部到局部收敛性，并在一般 $L^p$ 空间中证明了强收敛性及收敛速率。

Singular integrals in the rational Dunkl setting

On $\mathbb R^N$ equipped with a normalized root system $R$ and a multiplicity function $k\geq 0$ let us consider a (non-radial) kernel $K(\mathbf x)$ which has properties similar to those from the classical theory. We prove that a singular integral Dunkl convolution operator associated with the kernel $K$ is bounded on $L^p$ for $1<p<\infty$ and of weak-type (1,1). Further we study a maximal function related to the Dunkl convolutions with truncation of $K$.

On Finite Product of Convolutions and Classifications of Hyperbolic and Elliptic Equations

In this paper we consider the linear second order partial differential equation with non-constant coefficients; then by using the double convolution product we produce new equations with polynomials coefficients and we classify the new equations. It is shown that the classifications of hyperbolic and elliptic new equations are similar to the original equations that is the classification is invariant after finite double convolutions product.