Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derivatives of rational inner functions: geometry of singularities and
  integrability at the boundary   We analyze the singularities of rational inner functions on the unit bidisk
and study both when these functions belong to Dirichlet-type spaces and when
their partial derivatives belong to Hardy spaces. We characterize derivative
$H^{\mathfrak{p}}$ membership purely in terms of contact order, a measure of
the rate at which the zero set of a rational inner function approaches the
distinguished boundary of the bidisk. We also show that derivatives of rational
inner functions with singularities fail to be in $H^{\mathfrak{p}}$ for
$\mathfrak{p}\ge\frac{3}{2}$ and that higher non-tangential regularity of a
rational inner function paradoxically reduces the $H^{\mathfrak{p}}$
integrability of its derivative. We derive inclusion results for Dirichlet-type
spaces from derivative inclusion for $H^{\mathfrak{p}}$. Using Agler
decompositions and local Dirichlet integrals, we further prove that a
restricted class of rational inner functions fails to belong to the unweighted
Dirichlet space.

20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio