1. CMB Online first
 Hsu, MingHsiu; Lee, MingYi

VMO space associated with parabolic sections and its application
In this paper we define $VMO_\mathcal{P}$ space associated with
a family $\mathcal{P}$ of parabolic sections and show that the
dual of $VMO_\mathcal{P}$ is the Hardy space $H^1_\mathcal{P}$.
As an application, we prove that almost everywhere convergence
of a bounded sequence in $H^1_\mathcal{P}$ implies weak* convergence.
Keywords:MongeAmpere equation, parabolic section, Hardy space, BMO, VMO Category:42B30 

2. CMB 2012 (vol 56 pp. 647)
 Valverde, Cesar

On Induced Representations Distinguished by Orthogonal Groups
Let $F$ be a local nonarchimedean field of characteristic zero. We
prove that a representation of $GL(n,F)$ obtained from irreducible
parabolic induction of supercuspidal representations is distinguished
by an orthogonal group only if the inducing data is distinguished by
appropriate orthogonal groups. As a corollary, we get that an
irreducible representation induced from supercuspidals that is
distinguished by an orthogonal group is metic.
Keywords:distinguished representation, parabolic induction Category:22E50 

3. CMB 2011 (vol 56 pp. 44)
4. CMB 2011 (vol 54 pp. 396)
5. CMB 2009 (vol 52 pp. 521)
6. CMB 2009 (vol 52 pp. 175)
 Biswas, Indranil

Connections on a Parabolic Principal Bundle, II
In \emph{Connections on a parabolic principal bundle over a curve, I}
we defined connections on a parabolic
principal bundle. While connections on usual principal bundles are
defined as splittings of the Atiyah exact sequence, it was noted in
the above article that the Atiyah exact sequence does not generalize to
the parabolic principal bundles.
Here we show that a twisted version
of the Atiyah exact sequence generalizes to the context of
parabolic principal bundles. For usual principal bundles, giving a
splitting of this twisted Atiyah exact sequence is equivalent
to giving a splitting of the Atiyah exact sequence. Connections on
a parabolic principal bundle can be defined using the
generalization of the twisted Atiyah exact sequence.
Keywords:Parabolic bundle, Atiyah exact sequence, connection Categories:32L05, 14F05 

7. CMB 1999 (vol 42 pp. 463)
 Hofmann, Steve; Li, Xinwei; Yang, Dachun

A Generalized Characterization of Commutators of Parabolic Singular Integrals
Let $x=(x_1, \dots, x_n)\in\rz$ and $\dz_\lz x=(\lz^{\az_1}x_1,
\dots,\lz^{\az_n}x_n)$, where $\lz>0$ and $1\le \az_1\le\cdots
\le\az_n$. Denote $\az=\az_1+\cdots+\az_n$. We characterize those
functions $A(x)$ for which the parabolic Calder\'on commutator
$$
T_{A}f(x)\equiv \pv \int_{\mathbb{R}^n}
K(xy)[A(x)A(y)]f(y)\,dy
$$
is bounded on $L^2(\mathbb{R}^n)$, where $K(\dz_\lz x)=\lz^{\az1}K(x)$,
$K$ is smooth away from the origin and satisfies a certain cancellation
property.
Keywords:parabolic singular integral, commutator, parabolic $\BMO$ sobolev space, homogeneous space, T1theorem, symbol Category:42B20 
