Weighted norm inequalities for de Branges--Rovnyak spaces and their applications
| dc.creator | Baranov, Anton | |
| dc.creator | Fricain, Emmanuel | |
| dc.creator | Mashreghi, Javad | |
| dc.date | 2008-02-06 | |
| dc.date.accessioned | 2026-07-07T09:19:02Z | |
| dc.date.available | 2026-07-07T09:19:02Z | |
| dc.description | Let $\mathcal{H}(b)$ denote the de Branges--Rovnyak space associated with a function $b$ in the unit ball of $H^\infty(\mathbb{C}_+)$. We study the boundary behavior of the derivatives of functions in $\mathcal{H}(b)$ and obtain weighted norm estimates of the form $\|f^{(n)}\|_{L^2(μ)} \le C\|f\|_{\mathcal{H}(b)}$, where $f \in \mathcal{H}(b)$ and $μ$ is a Carleson-type measure on $\mathbb{C}_+\cup\mathbb{R}$. We provide several applications of these inequalities. We apply them to obtain embedding theorems for $\mathcal{H}(b)$ spaces. These results extend Cohn and Volberg--Treil embedding theorems for the model (star-invariant) subspaces which are special classes of de Branges--Rovnyak spaces. We also exploit the inequalities for the derivatives to study stability of Riesz bases of reproducing kernels $\{k^b_{λ_n}\}$ in $\mathcal{H}(b)$ under small perturbations of the points $λ_n$. | |
| dc.identifier | https://arxiv.org/abs/0802.0789 | |
| dc.identifier | http://arxiv.org/abs/0802.0789 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154240 | |
| dc.subject | Complex Variables | |
| dc.subject | Functional Analysis | |
| dc.title | Weighted norm inequalities for de Branges--Rovnyak spaces and their applications | |
| dc.type | text |