Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hyperbolic distance and membership of conformal maps in the Hardy space   Let $\psi$ be a conformal map of the unit disk $\mathbb{D}$ onto an unbounded
domain and, for $\alpha >0$, let ${F_\alpha }=\left\{ {z \in \mathbb{D}:\left|
{\psi \left( z \right)} \right| = \alpha } \right\}$. If ${H^p}\left(
\mathbb{D} \right)$ denotes the classical Hardy space and $d_\mathbb{D} {\left(
{0,{F_\alpha }} \right)}$ denotes the hyperbolic distance between $0$ and
$F_\alpha$ in $\mathbb{D}$, we prove that $\psi$ belongs to ${H^p}\left(
\mathbb{D} \right)$ if and only if
  \[\int_0^{ + \infty } {{\alpha ^{p - 1}}{e^{ - {d_{\mathbb{D}}}\left(
{0,{F_\alpha }} \right)}}d\alpha } < + \infty .\] This result answers a
question posed by P. Poggi-Corradini.

13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ