Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2019; 56(3): 745-756

Online first article December 14, 2018      Printed May 31, 2019

https://doi.org/10.4134/BKMS.b180540

Copyright © The Korean Mathematical Society.

Characterizations for the Fock-type spaces

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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