Mathematics – Complex Variables
Scientific paper
2008-02-06
Mathematics
Complex Variables
Scientific paper
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 $\|f^{(n)}\|_{L^2(\mu)} \le C\|f\|_{\mathcal{H}(b)}$, where $f \in \mathcal{H}(b)$ and $\mu$ 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 $\{k^b_{\lambda_n}\}$ in $\mathcal{H}(b)$ under small perturbations of the points $\lambda_n$.
Baranov Anton
Fricain Emmanuel
Mashreghi Javad
No associations
LandOfFree
Weighted norm inequalities for de Branges--Rovnyak spaces and their applications does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Weighted norm inequalities for de Branges--Rovnyak spaces and their applications, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Weighted norm inequalities for de Branges--Rovnyak spaces and their applications will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-559767