Abstract
In this paper, we give a characterization for the Fock-type space \({\mathcal{F}_{\alpha}^{\infty}(\mathbb{C}^N)}\) in terms of higher order derivatives of f and behaviors of local integral means of those derivatives. The space \({\mathcal{F}_{\alpha}^{\infty}(\mathbb{C}^N)}\) has the closed subspace \({\mathcal{F}_{\alpha, 0}^{\infty}(\mathbb{C}^N)}\). We also characterize this subspace via higher order derivatives. As an application we study the boundedness and compactness of the extended Cesaro operator T g on \({\mathcal{F}_{\alpha}^{\infty}(\mathbb{C}^N)}\) and \({\mathcal{F}_{\alpha, 0}^{\infty}(\mathbb{C}^N)}\).
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Ueki, Si. Higher Order Derivative Characterization for Fock-Type Spaces. Integr. Equ. Oper. Theory 84, 89–104 (2016). https://doi.org/10.1007/s00020-015-2246-1
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DOI: https://doi.org/10.1007/s00020-015-2246-1