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On an Interpolation Problem for the Classical Weighted Harmonic Bergman Space
We provide sufficient conditions for interpolating a sequence by a function belonging to the classical weighted harmonic Bergman space defined on the...
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Boundedness of weighted Hadamard–Bergman and weighted variable Hadamard–Bergman convolution operators
This paper is a continuation of recent studies of the class of Hadamard–Bergman operators presented in the works of Karapetyants and Samko (Complex...
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Weighted theory of Toeplitz operators on the Bergman space
We study the weighted compactness and boundedness properties of Toeplitz operators on the Bergman space with respect to Békollè-Bonami type weights....
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A representation for the reproducing kernel of a weighted Bergman space
For a weight function in the unit disk which is the modulus of a finite product of powers of Blaschke factors, we give a canonical representation for...
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Geometric characterizations for conformal map**s in weighted Bergman spaces
We prove that a conformal map** defined on the unit disk belongs to a weighted Bergman space if and only if certain integrals involving the...
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Uncertainty Principles and Differential Operators on the Weighted Bergman Space
We classify self-adjoint first-order differential operators on weighted Bergman spaces on the unit disc and answer questions related to uncertainty...
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Composition Operators on Weighted Bergman Spaces of Polydisk
We study composition operators between the weighted Bergman space of the polydisk and the weighted Bergman space of the unit disk. We find conditions...
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Hadamard–Bergman Operators on Weighted Spaces
This article continues the study of the Hadamard–Bergman operators in the unit disc of the complex plane. These operators arose as a natural...
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Product type operators acting between weighted Bergman spaces and Bloch type spaces
For analytic functions u , ψ in the unit disk ⅅ in the complex plane and an analytic self-map φ of ⅅ, we describe in this paper the boundedness and...
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Kernels of Toeplitz operators on the Bergman space
A Coburn theorem says that a nonzero Toeplitz operator on the Hardy space is one-to-one or its adjoint operator is one-to-one. We study the...
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Toeplitz operators on weighted Bergman spaces on finitely connected domains
We study the weighted Bergman spaces on finitely connected planar domains. They are isomorphic to the product of weighted Bergman spaces on the unit...
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2-Complex Symmetric Weighted Composition Operators on the Weighted Bergman Spaces of the Half-Plane
In the paper, 2-complex symmetric weighted composition operators induced by three type symbols on the weighted Bergman spaces of the right half-plane...
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The Hadamard–Bergman Convolution on the Half-Plane
We introduce the Hadamard–Bergman convolution on the half-plane. We show that it exists in terms of the Hadamard product and it is commutative on the...