Related papers: Homogeneous operators and homogeneous integral ope…
This article surveys results that relate homogenisation problems for partial differential equations and convergence in the weak operator topology of a suitable choice of linear operators. More precisely, well-known notions like…
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…
Recent advances in operator learning theory have improved our knowledge about learning maps between infinite dimensional spaces. However, for large-scale engineering problems such as concurrent multiscale simulation for mechanical…
The paper deals with homogenization of Levy-type operators with rapidly oscillating coefficients. We consider cases of periodic and random statistically homogeneous micro-structures and show that in the limit we obtain a Levy-operator. In…
We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and…
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
In this paper we define an integral operator on Lp and obtain its degree of convergence in the appropriate norm. By specializing the kernel of the integral operator we obtain many known results as corollaries. We have also applied our…
In the present paper the algebras of functions on quantum homogeneous spaces are studied. The author introduces the algebras of kernels of intertwining integral operators and constructs quantum analogues of the Poisson and Radon transforms…
There is a lot of information available concerning Hardy-Hilbert type inequalities in one or more dimensions. In this paper we introduce the development of such inequalities on homogeneous groups. Moreover, we point out a unification of…
In this short report we estimate and calculate the exact value of norms of multilinear integral operators having homogeneous kernel, acting between two Grand Lebesgue Spaces.
In this paper we study integral operators with kernels \begin{equation*} K(x,y)= k_1( x- A_1y)...k_m( x-A_my), \end{equation*} $k_i(x)=\frac{\Omega_i(x)}{|x|^{n/q_i}}$ where $\Omega_i: \mathbb{R}^n\to \mathbb{R}$ are homogeneous functions…
Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research…
We discuss when an operator, subject to a rather general inequality in hereditary form, admits a unitarily equivalent functional model of Agler type in the reproducing kernel Hilbert space associated to the inequality. To the contrary to…
We extend the recent results concerning boundedness of the maximal regularity operator on tent spaces. This leads us to develop a singular integral operator theory on tent spaces. Such operators have operator-valued kernels. A seemingly…
In this article we consider the classical singular integral operator over a local field with rough kernels. We study the boundedness of such an operator on different function spaces by relaxing the smoothness condition on kernels.
This paper investigates homogenization problems for the nonlocal operators with rapidly oscillating coefficients in the cases of periodic and random statistically homogeneous micro-structures. These operators involve the fractional…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
The aim of this paper is to introduce several notions of homogenization in various classes of weighted means, which include quasiarithmetic and semideviation means. In general, the homogenization is an operator which attaches a homogeneous…
In the theory of singular integral operators significant effort is often required to rigorously define such an operator. This is due to the fact that the kernels of such operators are not locally integrable on the diagonal, so the integral…
Kernel theorems, in general, provide a convenient representation of bounded linear operators. For the operator acting on a concrete function space, this means that its action on any element of the space can be expressed as a generalised…