Year: 2025
Type: preprint
Abstract: We study the cyclicity of multipliers in Dirichlet-type spaces \( D_α(\mathbb{B}_n) \). Specifically, we show that a multiplier \( f \) analytic on a neighborhood of $\overline{\mathbb{B}}_n$, whose zero set on the unit sphere is a compact, smooth, complex tangential submanifold of real dimension \( m \leq n - 1 \), is cyclic in \( D_α(\mathbb{B}_n) \) if and only if \( α\leq \frac{2n - m}{2} \). Our approach combines classical results on peak sets in \( A^\infty(\mathbb{B}_n) \) due to Chaumat and Chollet with a Corona-type theorem with two generators for the multiplier algebra.
Source: arXiv (Cornell University)
Author: Ziarati, Pouriya Torkinejad
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979265100
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