Related papers: On integral representation of radial operators
We prove a Fredholm criterion for operators in the Banach algebra of singular integral operators with matrix piecewise continuous coefficients acting on a variable Lebesgue space with a radial oscillating weight over a logarithmic Carleson…
The weighted numerical radius of a Hilbert space operator has been defined recently. This article explores other properties and uses this newly defined numerical radius to obtain several new interesting inequalities for the weighted…
We use the notion of radial derivative to introduce composition-differentiation operators on the Hardy and Bergman spaces of the unit ball and the polydisk. We seek for necessary and sufficient conditions on the inducing functions to ensure…
A consistent description of images on the disk and of their transformations is given as elements of a vector space and of an operators algebra. The vector space of images on the disk $\mathbb{D}$ is the Hilbert space $L^2(\mathbb{D})$ that…
This article develops a novel approach to the representation of singular integral operators of Calder\'on-Zygmund type in terms of continuous model operators, in both the classical and the bi-parametric setting. The representation is…
We obtain sampling and interpolation theorems in radial weighted spaces of analytic functions for weights of arbitrary (more rapid than polynomial) growth. We give an application to invariant subspaces of arbitrary index in large weighted…
In this paper we obtain a necessary and sufficient condition for the canonical solution operator to $\overline \partial $ restricted to radial symmetric Bergman spaces to be a Hilbert-Schmidt operator. We also discuss compactness of the…
We study the description of semicommutative Hardy spaces in terms of molecules. We use this characterization to obtain $\mathrm{H}_1^c - \mathrm{H}_1^c$ estimates for Calder\'on-Zygmund operators with kernels with values in a semifinite von…
The object of the present paper is to study of radius of convexity two certain integral operators as follows \begin{equation*} F(z):=\int_{0}^{z}\prod_{i=1}^{n}\left(f'_i(t)\right)^{\gamma_i}{\rm d}t \end{equation*} and \begin{equation*}…
We study singular Schr\"odinger operators on a finite interval as selfadjoint extensions of a symmetric operator. We give sufficient conditions for the symmetric operator to be in the $n$-entire class, which was defined in our previous…
In this paper, we prove the boundedness of multilinear fractional integral operators from products of Hardy spaces associated with ball quasi-Banach function spaces into their corresponding ball quasi-Banach function spaces. As…
In this paper we investigate the reproducing kernel Hilbert space where the polylogarithm appears as kernel functions. This investigation begins with the properties of functions in this space, and here a connection to the classical Hardy…
We characterize the dual spaces of the generalized Hardy spaces defined by replacing Lebesgue quasi-norms by Wiener amalgam ones. In these generalized Hardy spaces, we prove that some classical linear operators such as Calder\'on-Zygmund,…
We prove nontangential and radial maximal function characterizations for Hardy spaces associated to a non-negative self-adjoint operator satisfying Gaussian estimates on a space of homogeneous type with finite measure. This not only…
We consider the products of composition and differentiation operators on the Hardy space. We provide a complete characterization of the boundedness and compactness of these operators. Furthermore, we obtain the explicit condition for these…
In this paper, we present the current results in the study of weighted composition operators on the Bloch space of bounded homogeneous domains in $\mathbb{C}^n$ with particular emphasis on the issues of boundedness and compactness. We also…
In this paper, we show Hardy-Rellich identities for polyharmonic operators $\Delta^m$ and radial Laplacian $\Delta_r^m$ in $\mathbb{R}^n$ with Hardy-H\'enon weight $|x|^\alpha$ for all $m, n\in \mathbb{N}, \alpha\in \mathbb{R}$. Moreover,…
We work with very general Banach spaces of analytic functions in the disk or other domains which satisfy a minimum number of natural axioms. Among the preliminary results, we discuss some implications of the basic axioms and identify all…
We generalise the Riesz representation theorems for positive linear functionals on $\mathrm{C}_{\mathrm c}(X)$ and $\mathrm{C}_{\mathrm 0}(X)$, where $X$ is a locally compact Hausdorff space, to positive linear operators from these spaces…
We observe that local embedding problems for certain Hardy and Bergman spaces of Dirichlet series are equivalent to boundedness of a class of composition operators. Following this, we perform a careful study of such composition operators…