Nearly-optimal estimates for the stability problem in Hardy spaces
| dc.creator | Trong, Dang Duc | |
| dc.creator | Truong, Tuyen Trung | |
| dc.date | 2008-11-29 | |
| dc.date.accessioned | 2026-07-07T12:08:08Z | |
| dc.date.available | 2026-07-07T12:08:08Z | |
| dc.description | We continue the work of \cite{TLNT}. Let $E$ be a non-Blaschke subset of the unit disc $\mathbb{D}$ of the complex plane $\mathbb{C}$. Fixed $1\leq p\leq \infty$, let $H^p(\mathbb{D})$ be the Hardy space of holomorphic functions in the disk whose boundary value function is in $L^p(\partial \mathbb{D})$. Fixed $0<R<1$. For $ε>0$ define C_p(\varepsilon, R) = \sup \{\sup_{|z| \leq R}|g(z)|: g\in H^p, \|g\|_p\leq 1, |g(ζ)| \leq \varepsilon \forall ζ\in E\}. In this paper we find upper and lower bounds for $C_p(ε, R)$ when $ε$ is small for any non-Blaschke set $E$. The bounds are nearly-optimal for many such sets $E$, including sets contained in a compact subset of $\mathbb{D}$ and sets contained in a finite union of Stolz angles. | |
| dc.description | This is an extended and revised version of arXiv:math/0701044 | |
| dc.identifier | https://arxiv.org/abs/0812.0075 | |
| dc.identifier | http://arxiv.org/abs/0812.0075 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209214 | |
| dc.subject | Complex Variables | |
| dc.subject | 30D15, 31A15, 44A10, 65F22 | |
| dc.title | Nearly-optimal estimates for the stability problem in Hardy spaces | |
| dc.type | text |