تقرير
Bloch functions with wild boundary behaviour in $\mathbb{C}^N$
| العنوان: | Bloch functions with wild boundary behaviour in $\mathbb{C}^N$ |
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| المؤلفون: | Charpentier, Stéphane, Espoullier, Nicolas, Zarouf, Rachid |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Complex Variables |
| الوصف: | We prove the existence of functions $f$ in the Bloch space of the unit ball $\mathbb{B}_N$ of $\mathbb{C}^N$ with the property that, given any measurable function $\varphi$ on the unit sphere $\mathbb{S}_N$, there exists a sequence $(r_n)_n$, $r_n\in (0,1)$, converging to $1$, such that for every $w\in \mathbb{B}_N$, $$f(r_n(\zeta -w)+w) \to \varphi(\zeta)\text{ as }n\to \infty\text{, for almost every }\zeta \in \mathbb{S}_N.$$ The set of such functions is residual in the little Bloch space. A similar result is obtained for the Bloch space of the polydisc. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2407.08294 |
| رقم الأكسشن: | edsarx.2407.08294 |
| قاعدة البيانات: | arXiv |
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