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1. CMB Online first
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:Monge-Ampere equation, parabolic section, Hardy space, BMO, VMO Category:42B30 |
2. CMB 2012 (vol 56 pp. 647)
On Induced Representations Distinguished by Orthogonal Groups Let $F$ be a local non-archimedean 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)
Polystable Parabolic Principal $G$-Bundles and Hermitian-Einstein Connections We show that there
is a bijective correspondence between the polystable parabolic
principal $G$-bundles and solutions of the Hermitian-Einstein
equation.
Keywords:ramified principal bundle, parabolic principal bundle, Hitchin-Kobayashi correspondence, polystability Categories:32L04, 53C07 |
4. CMB 2011 (vol 54 pp. 396)
Parabolic Geodesics in Sasakian $3$-Manifolds We give explicit parametrizations for all
parabolic geodesics in 3-dimensional Sasakian space forms.
Keywords:parabolic geodesics, pseudo-Hermitian geometry, Sasakian manifolds Category:58E20 |
5. CMB 2009 (vol 52 pp. 521)
The Parabolic Littlewood--Paley Operator with Hardy Space Kernels In this paper, we give the $L^p$ boundedness for
a class of parabolic Littlewood--Paley $g$-function with its kernel
function $\Omega$ is in the Hardy space $H^1(S^{n-1})$.
Keywords:parabolic Littlewood-Paley operator, Hardy space, rough kernel Categories:42B20, 42B25 |
6. CMB 2009 (vol 52 pp. 175)
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)
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
$$
T_{A}f(x)\equiv \pv \int_{\mathbb{R}^n}
K(x-y)[A(x)-A(y)]f(y)\,dy
$$
is bounded on $L^2(\mathbb{R}^n)$, where $K(\dz_\lz x)=\lz^{-|\az|-1}K(x)$,
$K$ is smooth away from the origin and satisfies a certain cancellation
property.
Keywords:parabolic singular integral, commutator, parabolic $\BMO$ sobolev space, homogeneous space, T1-theorem, symbol Category:42B20 |