Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poincar\'e type inequalities for group measure spaces and related
  transportation cost inequalities   Let $G$ be a countable discrete group with an orthogonal representation
$\alpha$ on a real Hilbert space $H$. We prove $L_p$ Poincar\'e inequalities
for the group measure space $L_\infty(\Omega_H,\gamma)\rtimes G$, where both
the group action and the Gaussian measure space $(\Omega_H, \gamma)$ are
associated with the representation $\alpha$. The idea of proof comes from
Pisier's method on the boundedness of Riesz transform and Lust-Piquard's work
on spin systems. Then we deduce a transportation type inequality from the $L_p$
Poincar\'e inequalities in the general noncommutative setting. This inequality
is sharp up to a constant (in the Gaussian setting). Several applications are
given, including Wiener/Rademacher chaos estimation and new examples of
Rieffel's compact quantum metric spaces.

22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga