Related papers: On integral representation of radial operators
A radial weight $\omega$ belongs to the class $\widehat{\mathcal{D}}$ if there exists $C=C(\omega)\ge 1$ such that $\int_r^1 \omega(s)\,ds\le C\int_{\frac{1+r}{2}}^1\omega(s)\,ds$ for all $0\le r<1$. Write $\omega\in\check{\mathcal{D}}$ if…
We present some old and new results on a class of invariant spaces of holomorphic functions on symmetric domains, both in their circular bounded realizations and in their unbounded realizations as Siegel domains of type II. These spaces…
In this paper we characterize compact Hankel operators with conjugate holomorphic symbols on the Bergman space of bounded convex Reinhardt domains in $\mathbb{C}^2$. We also characterize compactness of Hankel operators with conjugate…
In this dissertation we explore the $[L^{\mathrm{p}},\ L^{q}]$-boundedness of certain integral operators on weighted spaces on cones in ${\mathbb R}^{n}.$ These integral operators are of the type $\displaystyle \int_{V}k(x,\ y)f(y)dy$…
For analytic functions $g$ on the unit disc with non-negative Maclaurin coefficients, we describe the boundedness and compactness of the integral operator $T_g(f)(z)=\int_0^zf(\zeta)g'(\zeta)\,d\zeta$ from a space $X$ of analytic functions…
We study the restriction operator from the Bergman space of a domain in $\mathbb{C}^n$ to the Bergman space of a non-empty open subset of the domain. We relate the restriction operator to the Toeplitz operator on the Bergman space of the…
The characterization of the boundedness of operators induced by Hankel matrices on analytic function spaces can be traced back to the work of Z. Nehari and H. Widom on the Hardy space, and has been extensively studied on many other analytic…
In the present work, we are interested in compact integration operators $I_g f(z) = \int_0^z f(\zeta)g'(\zeta)d\zeta$ acting on the Hardy space $H^2$ and on the weighted Bergman spaces $\mathcal{A}^2_\alpha$. We give upper and lower…
We introduce Hausdorff operators over the unit disc and give conditions for boundedness of such operator in Bloch, Bergman, and Hardy spaces on the disc. Identity approximation by Hausdorff operators is also considered.
We prove a number of results on integrability and extendability of Lie algebras of unbounded skew-symmetric operators with common dense domain in Hilbert space. By integrability for a Lie algebra $\mathfrak{g}$, we mean that there is an…
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 address the problem of studying the boundedness, compactness and weak compactness of the integral operators $T_g(f)(z)=\int_0^z f(\zeta)g'(\zeta)\,d\zeta$ acting from a Banach space $X$ into $H^\infty$. We obtain a collection of general…
We study compactness of Hankel and Toeplitz operators on Bergman spaces of convex Reinhardt domains in $\mathbb{C}^2$ and we restrict the symbols to the class of functions that are continuous on the closure of the domain. We prove that…
The purpose of the paper is to study the operators on the weighted Bergman spaces on the unit disk ${\mathbb{D}}$, denoted by $A^{p}_{\lambda,w}({\mathbb{D}})$, that are associated with a class of generalized analytic functions, named the…
The rational Dunkl operators are commuting differential-reflection operators on the Euclidean space $R^d$ associated with a root system, that contain some non-local refection terms, and the associated Hardy space is defined by means of the…
We construct explicit examples of non-trivial nilpotent Toeplitz operators on Bergman spaces of certain Reinhardt domains in $\mathbb{C}^2$.
We provide a representation of the $C^*$-algebra generated by multidimensional integral operators with piecewise constant kernels and discrete ergodic operators. This representation allows us to find the spectrum and to construct the…
In this paper we completely describe the numerical range of Toeplitz operators on weighted Bergman spaces with harmonic symbol. We also characterize the numerical range of weighted composition operators on weighted Bergman spaces and…
The boundedness and compactness of weighted composition operators on the Hardy space ${\mathcal H}^2$ of the unit disc is analysed. Particular reference is made to the case when the self-map of the disc is an inner function. Schatten-class…
We build on a characterization of inner functions $f$ due to Le, in terms of the spectral properties of the operator $V=M_f^*M_f$ and study to what extent the cyclicity on weighted Hardy spaces $H^2_\omega$ of the function $z \mapsto a-z$…