Characterizations for the Fock-type spaces
Bull. Korean Math. Soc. 2019 Vol. 56, No. 3, 745-756
Published online December 14, 2018
Printed May 31, 2019
Hong Rae Cho, Jeong Min Ha, Kyesook Nam
Pusan National University; Pusan National University; Seoul National University
Abstract : We obtain Lipschitz type characterization and double integral characterization for Fock-type spaces with the norm \begin{align*} \|f\|_{F_{m, \alpha,t}^{p}}^{p}=\incn \left| f(z)e^{-\alpha|z|^m} \right|^p\,\frac{dV(z)}{(1+|z|)^{t}}, \end{align*} where $\alpha>0$, $t\in \R$, and $m\in\mathbb{N}$. The results of this paper are the extensions of the classical weighted Fock space $F_{2, \alpha,t}^{p}$.
Keywords : Fock-type space, Lipschitz condition, double integral condition
MSC numbers : 32A37, 30H20
Supported by : The first author was supported by NRF of Korea (NRF-2016R1D1A1B03933740) and the third author was supported by NRF of Korea (NRF-2013R1A1A2057890)
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