New characterizations for Fock spaces

Release time:2025-02-13

Journal:Annales de l'Institut Fourier（Accepted）arXiv:2504.00545

Abstract:We show that the maximal Fock space F∞α on Cn is a Lipschitz space, that is, there exists a distance dα on Cn such that an entire function f on Cn belongs to F∞α if and only if |f(z)−f(w)|≤Cdα(z,w) for some constant C and all z,w∈Cn. This can be considered the Fock space version of the following classical result in complex analysis: a holomorphic function f on the unit ball Bn in Cn belongs to the Bloch space if and only if there exists a positive constant C such that |f(z)−f(w)|≤Cβ(z,w) for all z,w∈Bn, where β(z,w) is the distance on Bn in the Bergman metric. We also present a new approach to Hardy-Littlewood type characterizations for Fpα.

Co-author:Guanlong Bao, Pan Ma, Kehe Zhu

Indexed by:Journal paper

Discipline:Natural Science

First-Level Discipline:Mathematics

Document Type:J

Translation or Not:no

Included Journals:SCI