Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weighted norm inequalities for de Branges--Rovnyak spaces and their
  applications   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 $\lambda_n$.

27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th