Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitesimal Carleson property for weighted measures induced by
  analytic self-maps of the unit disk   We prove that, for every $\alpha > -1$, the pull-back measure $\phi ({\cal
A}_\alpha)$ of the measure $d{\cal A}_\alpha (z) = (\alpha + 1) (1 -
|z|^2)^\alpha \, d{\cal A} (z)$, where ${\cal A}$ is the normalized area
measure on the unit disk $\D$, by every analytic self-map $\phi \colon \D \to
\D$ is not only an $(\alpha + 2)$-Carleson measure, but that the measure of the
Carleson windows of size $\eps h$ is controlled by $\eps^{\alpha + 2}$ times
the measure of the corresponding window of size $h$. This means that the
property of being an $(\alpha + 2)$-Carleson measure is true at all
infinitesimal scales. We give an application by characterizing the compactness
of composition operators on weighted Bergman-Orlicz spaces.

10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org