1. CMB 2015 (vol 58 pp. 507)
 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 2014 (vol 58 pp. 432)
 Yang, Dachun; Yang, Sibei

Secondorder Riesz Transforms and Maximal Inequalities Associated with Magnetic SchrÃ¶dinger Operators
Let $A:=(\nablai\vec{a})\cdot(\nablai\vec{a})+V$ be a
magnetic SchrÃ¶dinger operator on $\mathbb{R}^n$,
where $\vec{a}:=(a_1,\dots, a_n)\in L^2_{\mathrm{loc}}(\mathbb{R}^n,\mathbb{R}^n)$
and $0\le V\in L^1_{\mathrm{loc}}(\mathbb{R}^n)$ satisfy some reverse
HÃ¶lder conditions.
Let $\varphi\colon \mathbb{R}^n\times[0,\infty)\to[0,\infty)$ be such that
$\varphi(x,\cdot)$ for any given $x\in\mathbb{R}^n$ is an Orlicz function,
$\varphi(\cdot,t)\in {\mathbb A}_{\infty}(\mathbb{R}^n)$ for all $t\in (0,\infty)$
(the class of uniformly Muckenhoupt weights) and its uniformly critical upper type index
$I(\varphi)\in(0,1]$. In this article, the authors prove that
secondorder Riesz transforms $VA^{1}$ and
$(\nablai\vec{a})^2A^{1}$ are bounded from the
MusielakOrliczHardy space $H_{\varphi,\,A}(\mathbb{R}^n)$, associated with $A$,
to the MusielakOrlicz space $L^{\varphi}(\mathbb{R}^n)$. Moreover, the authors
establish the boundedness of $VA^{1}$ on $H_{\varphi, A}(\mathbb{R}^n)$. As applications, some
maximal inequalities associated with $A$ in the scale of $H_{\varphi,
A}(\mathbb{R}^n)$ are obtained.
Keywords:MusielakOrliczHardy space, magnetic SchrÃ¶dinger operator, atom, secondorder Riesz transform, maximal inequality Categories:42B30, 42B35, 42B25, 35J10, 42B37, 46E30 

3. CMB 2011 (vol 56 pp. 229)
 Arvanitidis, Athanasios G.; Siskakis, Aristomenis G.

CesÃ ro Operators on the Hardy Spaces of the HalfPlane
In this article we study the CesÃ ro
operator
$$
\mathcal{C}(f)(z)=\frac{1}{z}\int_{0}^{z}f(\zeta)\,d\zeta,
$$
and its companion operator $\mathcal{T}$ on Hardy spaces of the
upper half plane. We identify $\mathcal{C}$ and $\mathcal{T}$ as
resolvents for appropriate semigroups of composition operators and we
find the norm and the spectrum in each case. The relation of
$\mathcal{C}$ and $\mathcal{T}$ with the corresponding Ces\`{a}ro
operators on Lebesgue spaces $L^p(\mathbb R)$ of the boundary line is also
discussed.
Keywords:CesÃ ro operators, Hardy spaces, semigroups, composition operators Categories:47B38, 30H10, 47D03 

4. CMB 2011 (vol 55 pp. 303)
 Han, Yongsheng; Lee, MingYi; Lin, ChinCheng

Atomic Decomposition and Boundedness of Operators on Weighted Hardy Spaces
In this article, we establish a new atomic decomposition for $f\in L^2_w\cap H^p_w$,
where the decomposition converges in $L^2_w$norm rather than in the distribution sense.
As applications of this decomposition, assuming that $T$ is a linear
operator bounded on $L^2_w$ and $0
Keywords:$A_p$ weights, atomic decomposition, CalderÃ³n reproducing formula, weighted Hardy spaces Categories:42B25, 42B30 

5. CMB 2010 (vol 54 pp. 159)
 Sababheh, Mohammad

Hardy Inequalities on the Real Line
We prove that some inequalities, which are considered to be
generalizations of Hardy's inequality on the circle,
can be modified and proved to be true for functions integrable on the real line.
In fact we would like to show that some constructions that were
used to prove the Littlewood conjecture can be used similarly to
produce real Hardytype inequalities.
This discussion will lead to many questions concerning the
relationship between Hardytype inequalities on the circle and
those on the real line.
Keywords:Hardy's inequality, inequalities including the Fourier transform and Hardy spaces Categories:42A05, 42A99 

6. CMB 2009 (vol 52 pp. 521)
7. CMB 2006 (vol 49 pp. 381)
8. CMB 2005 (vol 48 pp. 370)
 Daly, J. E.; Fridli, S.

Trigonometric Multipliers on $H_{2\pi}$
In this paper we consider multipliers on the real Hardy space
$H_{2\pi}$. It is known that the Marcinkiewicz and the
H\"ormanderMihlin conditions are sufficient for the corresponding
trigonometric multiplier to be bounded on $L_{2\pi}^p$, $1
Keywords:Multipliers, Hardy space Categories:42A45, 42A50, 42A85 

9. CMB 1999 (vol 42 pp. 97)
 Kwon, E. G.

On Analytic Functions of Bergman $\BMO$ in the Ball
Let $B = B_n$ be the open unit ball of $\bbd C^n$ with
volume measure $\nu$, $U = B_1$ and ${\cal B}$ be the Bloch space on
$U$. ${\cal A}^{2, \alpha} (B)$, $1 \leq \alpha < \infty$, is defined
as the set of holomorphic $f\colon B \rightarrow \bbd C$ for which
$$
\int_B \vert f(z) \vert^2 \left( \frac 1{\vert z\vert}
\log \frac 1{1  \vert z\vert } \right)^{\alpha}
\frac {d\nu (z)}{1\vert z\vert} < \infty
$$
if $0 < \alpha <\infty$ and ${\cal A}^{2, 1} (B) = H^2(B)$, the Hardy
space. Our objective of this note is to characterize, in terms of
the Bergman distance, those holomorphic $f\colon B \rightarrow U$ for
which the composition operator $C_f \colon {\cal B} \rightarrow
{\cal A}^{2, \alpha}(B)$ defined by $C_f (g) = g\circ f$,
$g \in {\cal B}$, is bounded. Our result has a corollary that
characterize the set of analytic functions of bounded mean
oscillation with respect to the Bergman metric.
Keywords:Bergman distance, \BMOA$, Hardy space, Bloch function Category:32A37 

10. CMB 1998 (vol 41 pp. 404)
 AlHasan, Abdelnaser J.; Fan, Dashan

$L^p$boundedness of a singular integral operator
Let $b(t)$ be an $L^\infty$ function on $\bR$, $\Omega (\,y')$ be
an $H^1$ function on the unit sphere satisfying the mean zero
property (1) and $Q_m(t)$ be a real polynomial on $\bR$ of degree
$m$ satisfying $Q_m(0)=0$. We prove that the singular integral
operator
$$
T_{Q_m,b} (\,f) (x)=p.v. \int_\bR^n b(y) \Omega(\,y) y^{n} f
\left( xQ_m (y) y' \right) \,dy
$$
is bounded in $L^p (\bR^n)$ for $1
Keywords:singular integral, rough kernel, Hardy space Category:42B20 

11. CMB 1998 (vol 41 pp. 196)
 Nakazi, Takahiko

BrownHalmos type theorems of weighted Toeplitz operators
The spectra of the Toeplitz operators on the weighted Hardy space
$H^2(Wd\th/2\pi)$ and the Hardy space $H^p(d\th/2\pi)$, and the
singular integral operators on the Lebesgue space $L^2(d\th/2\pi)$
are studied. For example, the theorems of BrownHalmos type and
HartmanWintner type are studied.
Keywords:Toeplitz operator, singular integral, operator, weighted Hardy space, spectrum. Category:47B35 

12. CMB 1997 (vol 40 pp. 475)
 Lou, Zengjian

Coefficient multipliers of Bergman spaces $A^p$, II
We show that the multiplier space $(A^1,X)=\{g:M_\infty(r,g'')
=O(1r)^{1}\}$, where $X$ is $\BMOA$, $\VMOA$, $B$, $B_0$ or disk algebra $A$.
We give the multipliers from $A^1$ to $A^q(H^q)(1\le q\le \infty)$, we
also give the multipliers from $l^p(1\le p\le 2), C_0, \BMOA$, and
$H^p(2\le p<\infty)$ into $A^q(1\le q\le 2)$.
Keywords:Multiplier, Bergman space, Hardy space, Bloch space, $\BMOA$. Categories:30H05, 30B10 
