2025/04/01 by Guanlong Bao, Bao, Guanlong, Pan Ma +3
Mathematics · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2504.00545
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.