C ${\mathbb {C}}^N$

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-04-02 DOI:10.1112/blms.70055

Stéphane Charpentier, Nicolas Espoullier, Rachid Zarouf

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引用次数: 0

摘要

证明了C N$ {\mathbb {C}}^N$的单位球B N$ {\mathbb {B}}_N$的Bloch空间中函数f$ f$的存在性，其性质是：给定单位球面上任意可测函数φ $\varphi$ {\mathbb {S}}_N$，存在一个序列（r n） n$ (r_n)_n$，R n∈(0,1)$ r_n\in(0,1)$，收敛于1，使得对于每个w∈B N$ w\in {\mathbb {B}}_N$，

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$Bloch functions with wild boundary behavior in C N ${\mathbb {C}}^N$$

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Bloch functions with wild boundary behavior in C N ${\mathbb {C}}^N$

We prove the existence of functions $f$ in the Bloch space of the unit ball $B_{N}$ of $C^{N}$ with the property that, given any measurable function $φ$ on the unit sphere $S_{N}$ , there exists a sequence ${(r_{n})}_{n}$ , $r_{n} \in (0, 1)$ , converging to 1, such that for every $w \in B_{N}$ ,