1. CMB Online first
 Bu, Shangquan; Cai, Gang

Periodic solutions of second order degenerate differential equations with delay in Banach spaces
We give necessary and sufficient
conditions of the $L^p$wellposedness (resp. $B_{p,q}^s$wellposedness) for the second order degenerate
differential equation with finite delays:
$(Mu)''(t)+Bu'(t)+Au(t)=Gu'_t+Fu_t+f(t),(t\in [0,2\pi])$ with periodic
boundary conditions $(Mu)(0)=(Mu)(2\pi)$, $(Mu)'(0)=(Mu)'(2\pi)$, where
$A, B, M$ are closed linear operators on a complex Banach space $X$ satisfying
$D(A)\cap D(B)\subset D(M)$, $F$ and $G$ are bounded linear operators from
$L^p([2\pi,0];X)$ (resp. $B_{p,q}^s([2\pi,0];X)$) into $X$.
Keywords:second order degenerate differential equation, Fourier multiplier theorem, wellposedness, LebesgueBochner space, Besov space Categories:34G10, 34K30, 43A15, 47D06 

2. CMB Online first
 Wang, Lian Daniel

A Multiplier Theorem on Anisotropic Hardy Spaces
We present a multiplier theorem on anisotropic
Hardy spaces. When $m$ satisfies the anisotropic, pointwise Mihlin
condition, we obtain boundedness of the multiplier operator $T_m
: H_A^p (\mathbb R^n) \rightarrow H_A^p (\mathbb R^n)$, for the range of $p$
that depends on the eccentricities of the dilation $A$ and the
level of regularity of a multiplier symbol $m$. This extends
the classical multiplier theorem of Taibleson and Weiss.
Keywords:anisotropic Hardy space, multiplier, Fourier transform Categories:42B30, 42B25, 42B35 

3. CMB Online first
 Bu, Shangquan; Cai, Gang

HÃ¶lder continuous solutions of degenerate differential equations with finite delay
Using known operatorvalued Fourier multiplier results on vectorvalued
HÃ¶lder continuous function spaces $C^\alpha (\mathbb R; X)$, we completely
characterize the $C^\alpha$wellposedness of the first order
degenerate differential equations with finite delay $(Mu)'(t)
= Au(t) + Fu_t + f(t)$ for $t\in\mathbb R$
by the boundedness of the $(M, F)$resolvent of $A$ under suitable
assumption on the delay operator $F$, where $A, M$ are closed
linear
operators on a Banach space $X$ satisfying $D(A)\cap D(M) \not=\{0\}$,
the delay operator $F$ is a bounded linear operator
from $C([r, 0]; X)$ to $X$ and $r \gt 0$ is fixed.
Keywords:wellposedness, degenerate differential equation, $\dot{C}^\alpha$multiplier, HÃ¶lder continuous function space Categories:34N05, 34G10, 47D06, 47A10, 34K30 

4. CMB 2011 (vol 55 pp. 708)
5. CMB 2011 (vol 54 pp. 654)
 Forrest, Brian E.; Runde, Volker

Norm One Idempotent $cb$Multipliers with Applications to the Fourier Algebra in the $cb$Multiplier Norm
For a locally compact group $G$, let $A(G)$ be its Fourier algebra, let $M_{cb}A(G)$ denote the completely
bounded multipliers of $A(G)$, and let $A_{\mathit{Mcb}}(G)$ stand for the closure of $A(G)$ in $M_{cb}A(G)$. We
characterize the norm one idempotents in $M_{cb}A(G)$: the indicator function of a set $E \subset G$ is a norm
one idempotent in $M_{cb}A(G)$ if and only if $E$ is a coset of an open subgroup of $G$. As applications, we
describe the closed ideals of $A_{\mathit{Mcb}}(G)$ with an approximate identity bounded by $1$, and we characterize
those $G$ for which $A_{\mathit{Mcb}}(G)$ is $1$amenable in the sense of B. E. Johnson. (We can even slightly
relax the norm bounds.)
Keywords:amenability, bounded approximate identity, $cb$multiplier norm, Fourier algebra, norm one idempotent Categories:43A22, 20E05, 43A30, 46J10, 46J40, 46L07, 47L25 

6. CMB 2011 (vol 55 pp. 260)
 Delvaux, L.; Van Daele, A.; Wang, Shuanhong

A Note on the Antipode for Algebraic Quantum Groups
Recently, Beattie, Bulacu ,and Torrecillas proved Radford's formula for the fourth power of the antipode for a coFrobenius Hopf algebra.
In this note, we show that this formula can be proved for any regular multiplier Hopf
algebra with integrals (algebraic quantum groups). This, of course, not only includes the case of a
finitedimensional Hopf algebra, but also that of any
Hopf algebra with integrals (coFrobenius Hopf algebras). Moreover, it turns out that
the proof in this more general situation, in fact, follows in a few lines from wellknown formulas obtained earlier in the
theory of regular multiplier Hopf algebras with integrals.
We discuss these formulas and their importance in this theory. We also mention their generalizations, in particular to the (in a certain sense) more general theory of locally compact quantum groups. Doing so, and also because the proof of the main result itself is very short, the present note becomes largely of an expository nature.
Keywords:multiplier Hopf algebras, algebraic quantum groups, the antipode Categories:16W30, 46L65 

7. CMB 2009 (vol 52 pp. 564)
 Jin, Hai Lan; Doh, Jaekyung; Park, Jae Keol

Group Actions on QuasiBaer Rings
A ring $R$ is called {\it quasiBaer} if the right
annihilator of every right ideal of $R$ is generated by an
idempotent as a right ideal. We investigate the quasiBaer
property of skew group rings and fixed rings under a finite group
action on a semiprime ring and their applications to
$C^*$algebras.
Various examples to illustrate and
delimit our results are provided.
Keywords:(quasi) Baer ring, fixed ring, skew group ring, $C^*$algebra, local multiplier algebra Categories:16S35, 16W22, 16S90, 16W20, 16U70 

8. CMB 2008 (vol 51 pp. 487)
9. 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 

10. CMB 2002 (vol 45 pp. 265)
 Nawrocki, Marek

On the Smirnov Class Defined by the Maximal Function
H.~O.~Kim has shown that contrary to the case of
$H^p$space, the Smirnov class $M$ defined by the radial maximal
function is essentially smaller than the classical Smirnov class
of the disk. In the paper we show that these two classes have the
same corresponding locally convex structure, {\it i.e.} they have the
same dual spaces and the same Fr\'echet envelopes. We describe a
general form of a continuous linear functional on $M$ and
multiplier from $M$ into $H^p$, $0 < p \leq \infty$.
Keywords:Smirnov class, maximal radial function, multipliers, dual space, FrÃ©chet envelope Categories:46E10, 30A78, 30A76 

11. 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 
