BLOCH FUNCTIONS IN THE BALL WITH UNIVERSAL NON-TANGENTIAL LIMITS
Résumé
We prove the existence of functions $f$ in the little Bloch space of the unit ball $\mathbb{B_n}$ of $\mathbb{C^n}$ with the property that, given any measurable function φ on the unit sphere $\mathbb{S_n}$, there exist a sequence (${r_n}$)$_n$, ${r_n}$ ∈ (0,1), converging to $1$, such that for every $z$ ∈ $\mathbb{B_n}$,
\[
f(r_n(\zeta -z)+z) \to φ(\zeta)\text{ as }n\to \infty\text{, for almost every }\zeta \in \S_n.
\]
The set of such functions is residual in the little Bloch space.
Domaines
Variables complexes [math.CV]Origine | Fichiers produits par l'(les) auteur(s) |
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