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Bull. Korean Math. Soc. 2022; 59(6): 1371-1385

Online first article September 13, 2022      Printed November 30, 2022

https://doi.org/10.4134/BKMS.b210783

Copyright © The Korean Mathematical Society.

Lipschitz type characterization of Fock type spaces

Hong Rae Cho, Jeong Min Ha

Pusan National University; Pusan National University

Abstract

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For setting a general weight function on $n$ dimensional complex space ${\mathbb C}^n$, we expand the classical Fock space.
We define Fock type space $F^{p,q}_{\phi, t}({\mathbb C}^n)$ of entire functions with a mixed norm, where $0<p,q<\infty$ and $t\in\mathbb R$ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{\phi, t}({\mathbb C}^n)$.
As a result of this application, the space $F^{p,p}_{\phi, t}({\mathbb C}^n)$ is especially characterized by a Lipschitz type condition.

Keywords: Fock type space, norm equivalence, Littlewood-Paley formula, Lipschitz type condition

MSC numbers: 32A37, 30H20

Supported by: The first author was financially supported by NRF-2020R1F1A1A0104860111 and the second author was financially supported by NRF-2021R1A2B5B03087097.

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