1. CMB Online first
 Bao, Guanlong; Göğüş, Nıhat Gökhan; Pouliasis, Stamatis

$\mathcal{Q}_p$ spaces and Dirichlet type spaces
In this paper, we show that the MÃ¶bius invariant
function space $\mathcal {Q}_p$ can be generated by variant
Dirichlet type spaces
$\mathcal{D}_{\mu, p}$ induced by finite positive Borel measures
$\mu$ on the open unit disk. A criterion for the equality between
the space $\mathcal{D}_{\mu, p}$ and the usual Dirichlet type
space $\mathcal {D}_p$ is given. We obtain a sufficient condition
to construct different $\mathcal{D}_{\mu, p}$ spaces
and we provide examples.
We establish decomposition theorems for $\mathcal{D}_{\mu,
p}$ spaces, and prove that the nonHilbert space $\mathcal
{Q}_p$ is equal to the intersection of Hilbert spaces $\mathcal{D}_{\mu,
p}$. As an application of the relation between $\mathcal {Q}_p$
and $\mathcal{D}_{\mu, p}$ spaces, we also obtain that there
exist different $\mathcal{D}_{\mu, p}$ spaces; this is a trick
to prove the existence without constructing examples.
Keywords:$\mathcal {Q}_p$ space, Dirichlet type space, MÃ¶bius invariant function space Categories:30H25, 31C25, 46E15 

2. CMB Online first
 Sickel, Winfried; Yang, Dachun; Yuan, Wen; Zhuo, Ciqiang

Characterizations of BesovType and TriebelLizorkinType Spaces via Averages on Balls
Let $\ell\in\mathbb N$ and $\alpha\in (0,2\ell)$. In this article,
the authors establish
equivalent characterizations
of Besovtype spaces, TriebelLizorkintype
spaces and BesovMorrey spaces via the sequence
$\{fB_{\ell,2^{k}}f\}_{k}$ consisting of the difference between
$f$ and
the ball average $B_{\ell,2^{k}}f$. These results give a way
to introduce Besovtype spaces,
TriebelLizorkintype spaces and BesovMorrey spaces with any
smoothness order
on metric measure spaces. As special cases, the authors obtain
a new characterization of MorreySobolev spaces
and $Q_\alpha$ spaces with $\alpha\in(0,1)$, which are of independent
interest.
Keywords:Besov space, TriebelLizorkin space, ball average, CalderÃ³n reproducing formula Categories:42B25, 46E35, 42B35 

3. CMB Online first
 Chen, ChungChuan

Disjoint hypercyclicity and weighted translations on discrete groups
Let $1\leq p\lt \infty$, and let $G$ be a discrete group. We give
a sufficient and necessary condition
for weighted translation operators on the Lebesgue space $\ell^p(G)$
to be densely disjoint hypercyclic.
The characterization for the dual of a weighted translation to
be densely disjoint hypercyclic is also obtained.
Keywords:disjoint hypercyclicity, topological transitivity, weighted translation, $\ell^p$space Categories:47A16, 47B38, 43A15 

4. CMB 2016 (vol 60 pp. 131)
5. CMB 2016 (vol 60 pp. 217)
 Wang, Yuanyi

Condition $C'_{\wedge}$ of Operator Spaces
In this paper, we study condition $C'_{\wedge}$ which is a
projective tensor product analogue of condition $C'$. We show
that
the finitedimensional OLLP operator spaces have condition
$C'_{\wedge}$ and $M_{n}$ $(n\gt 2)$ does not have that property.
Keywords:operator space, local theory, tensor product Category:46L07 

6. CMB 2016 (vol 60 pp. 104)
7. CMB Online first
 Iena, Oleksandr; Leytem, Alain

On the singular sheaves in the fine Simpson moduli spaces of $1$dimensional sheaves
In the Simpson moduli space $M$ of semistable sheaves with
Hilbert polynomial $dm1$ on a projective plane we study the
closed subvariety $M'$ of sheaves that are not locally free on
their support. We show that for $d\ge 4$ it is a singular subvariety
of codimension $2$ in $M$. The blow up of $M$ along $M'$ is interpreted
as a (partial) modification of $M\setminus M'$ by line bundles
(on support).
Keywords:Simpson moduli spaces, coherent sheaves, vector bundles on curves, singular sheaves Category:14D20 

8. CMB Online first
 Liu, Feng; Wu, Huoxiong

Endpoint Regularity of Multisublinear Fractional Maximal Functions
In this paper we investigate
the endpoint regularity properties of the multisublinear
fractional maximal operators, which include the multisublinear
HardyLittlewood maximal operator. We obtain some new bounds
for the derivative of the onedimensional multisublinear
fractional maximal operators acting on vectorvalued function
$\vec{f}=(f_1,\dots,f_m)$ with all $f_j$ being $BV$functions.
Keywords:multisublinear fractional maximal operators, Sobolev spaces, bounded variation Categories:42B25, 46E35 

9. CMB 2016 (vol 59 pp. 813)
10. CMB Online first
11. CMB 2016 (vol 60 pp. 77)
 Christ, Michael; Rieffel, Marc A.

Nilpotent Group C*algebras as Compact Quantum Metric Spaces
Let $\mathbb{L}$ be a length function on a group $G$, and let $M_\mathbb{L}$
denote the
operator of pointwise multiplication by $\mathbb{L}$ on $\lt(G)$.
Following Connes,
$M_\mathbb{L}$ can be used as a ``Dirac'' operator for the reduced
group C*algebra $C_r^*(G)$. It defines a
Lipschitz seminorm on $C_r^*(G)$, which defines a metric on the
state space of
$C_r^*(G)$. We show that
for any length function satisfying a strong form of polynomial
growth on a discrete group,
the topology from this metric
coincides with the
weak$*$ topology (a key property for the
definition of a ``compact quantum metric
space''). In particular, this holds for all wordlength functions
on finitely generated nilpotentbyfinite groups.
Keywords:group C*algebra, Dirac operator, quantum metric space, discrete nilpotent group, polynomial growth Categories:46L87, 20F65, 22D15, 53C23, 58B34 

12. CMB 2016 (vol 59 pp. 834)
 Liao, Fanghui; Liu, Zongguang

Some Properties of TriebelLizorkin and Besov Spaces Associated with Zygmund Dilations
In this paper, using CalderÃ³n's
reproducing formula and almost orthogonality estimates, we
prove the lifting property and the embedding theorem of the TriebelLizorkin
and Besov spaces associated with Zygmund dilations.
Keywords:TriebelLizorkin and Besov spaces, Riesz potential, CalderÃ³n's reproducing formula, almost orthogonality estimate, Zygmund dilation, embedding theorem Categories:42B20, 42B35 

13. CMB 2016 (vol 60 pp. 111)
 Ghaani Farashahi, Arash

Abstract Plancherel (Trace) Formulas over Homogeneous Spaces of Compact Groups
This paper introduces a unified operator theory approach to the
abstract Plancherel (trace) formulas over
homogeneous spaces of compact groups. Let $G$ be a compact group
and $H$ be a closed subgroup of $G$.
Let $G/H$ be the left coset space of $H$ in $G$ and $\mu$ be
the normalized $G$invariant measure on $G/H$ associated to the
Weil's formula.
Then, we present a generalized abstract notion of Plancherel
(trace) formula for the Hilbert space $L^2(G/H,\mu)$.
Keywords:compact group, homogeneous space, dual space, Plancherel (trace) formula Categories:20G05, 43A85, 43A32, 43A40 

14. CMB 2016 (vol 59 pp. 673)
 Bačák, Miroslav; Kovalev, Leonid V.

Lipschitz Retractions in Hadamard Spaces Via Gradient Flow Semigroups
Let $X(n),$ for $n\in\mathbb{N},$ be the set of all subsets of a metric
space $(X,d)$ of cardinality at most $n.$ The set $X(n)$ equipped
with the Hausdorff metric is called a finite subset space. In
this paper we are concerned with the existence of Lipschitz retractions
$r\colon X(n)\to X(n1)$ for $n\ge2.$ It is known that such retractions
do not exist if $X$ is the onedimensional sphere. On the other
hand L. Kovalev has recently established their existence in case $X$
is a Hilbert space and he also posed a question as to whether
or not such Lipschitz retractions exist for $X$ being a Hadamard
space. In the present paper we answer this question in the positive.
Keywords:finite subset space, gradient flow, Hadamard space, LieTrotterKato formula, Lipschitz retraction Categories:53C23, 47H20, 54E40, 58D07 

15. CMB 2016 (vol 59 pp. 769)
 GarcíaPacheco, Francisco Javier; Hill, Justin R.

Geometric Characterizations of Hilbert Spaces
We study some geometric properties related to the set $\Pi_X:=
\{
(x,x^*
)\in\mathsf{S}_X\times \mathsf{S}_{X^*}:x^*
(x
)=1
\}$ obtaining two characterizations of Hilbert spaces
in the category of Banach spaces. We also compute the distance
of a generic element $
(h,k
)\in H\oplus_2 H$ to $\Pi_H$ for $H$ a Hilbert space.
Keywords:Hilbert space, extreme point, smooth, $\mathsf{L}^2$summands Categories:46B20, 46C05 

16. CMB 2016 (vol 59 pp. 606)
 Mihăilescu, Mihai; Moroşanu, Gheorghe

Eigenvalues of $ \Delta_p \Delta_q $ Under Neumann Boundary Condition
The
eigenvalue problem $\Delta_p u\Delta_q u=\lambdau^{q2}u$
with $p\in(1,\infty)$, $q\in(2,\infty)$, $p\neq q$ subject to
the
corresponding homogeneous Neumann boundary condition is
investigated on a bounded open set with smooth boundary from
$\mathbb{R}^N$ with $N\geq 2$. A careful analysis of this problem leads
us to a complete description of the set of eigenvalues as being
a
precise interval $(\lambda_1, +\infty )$ plus an isolated point
$\lambda =0$. This comprehensive result is strongly related to
our
framework which is complementary to the wellknown case $p=q\neq
2$ for which a full description of the set of eigenvalues is
still
unavailable.
Keywords:eigenvalue problem, Sobolev space, Nehari manifold, variational methods Categories:35J60, 35J92, 46E30, 49R05 

17. CMB 2016 (vol 59 pp. 878)
 Wang, Jianfei

The Carleson Measure Problem Between Analytic Morrey Spaces
The purpose of this paper is to characterize positive measure
$\mu$ on the unit disk such that the analytic
Morrey space $\mathcal{AL}_{p,\eta}$ is boundedly and compactly
embedded to the tent space
$\mathcal{T}_{q,1\frac{q}{p}(1\eta)}^{\infty}(\mu)$ for the
case $1\leq q\leq p\lt \infty$
respectively. As an application, these results are used to
establish the boundedness and compactness of integral operators
and multipliers between analytic Morrey spaces.
Keywords:Morrey space, Carleson measure problem, boundedness, compactness Categories:30H35, 28A12, 47B38, 46E15 

18. CMB 2015 (vol 58 pp. 692)
 Anona, F. M.; Randriambololondrantomalala, Princy; Ravelonirina, H. S. G.

Sur les algÃ¨bres de Lie associÃ©es Ã une connexion
Let $\Gamma$ be a connection on a smooth manifold
$M$, in this paper we give some properties of $\Gamma$ by studying
the corresponding Lie algebras. In particular, we compute the
first ChevalleyEilenberg cohomology space of the horizontal
vector fields Lie algebra on the tangent bundle of $M$, whose
the corresponding Lie derivative of $\Gamma$ is null, and of
the horizontal nullity curvature space.
Keywords:algÃ¨bre de Lie, connexion, cohomologie de ChevalleyEilenberg, champs dont la dÃ©rivÃ©e de Lie correspondante Ã une connexion est nulle, espace de nullitÃ© de la courbure Categories:17B66, 53B15 

19. CMB 2015 (vol 59 pp. 104)
 He, Ziyi; Yang, Dachun; Yuan, Wen

LittlewoodPaley Characterizations of SecondOrder Sobolev Spaces via Averages on Balls
In this paper, the authors characterize secondorder Sobolev
spaces $W^{2,p}({\mathbb R}^n)$,
with $p\in [2,\infty)$ and $n\in\mathbb N$ or $p\in (1,2)$ and
$n\in\{1,2,3\}$, via the Lusin area
function and the LittlewoodPaley $g_\lambda^\ast$function in
terms of ball means.
Keywords:Sobolev space, ball means, Lusinarea function, $g_\lambda^*$function Categories:46E35, 42B25, 42B20, 42B35 

20. CMB 2015 (vol 59 pp. 3)
 Alfuraidan, Monther Rashed

The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph
We study the existence of fixed points for contraction multivalued
mappings in modular metric spaces endowed with a graph. The
notion of a modular metric on an arbitrary set and the corresponding
modular spaces, generalizing classical modulars over linear spaces
like Orlicz spaces, were recently introduced. This paper can
be seen as a generalization of Nadler's and Edelstein's fixed
point theorems to modular metric spaces endowed with a graph.
Keywords:fixed point theory, modular metric spaces, multivalued contraction mapping, connected digraph. Categories:47H09, 46B20, 47H10, 47E10 

21. CMB 2015 (vol 58 pp. 757)
22. CMB 2015 (vol 58 pp. 459)
 Casini, Emanuele; Miglierina, Enrico; Piasecki, Lukasz

Hyperplanes in the Space of Convergent Sequences and Preduals of $\ell_1$
The main aim of the present paper is to investigate various structural
properties
of hyperplanes of $c$, the Banach space of the convergent sequences.
In particular, we give an explicit formula for the projection
constants and we prove that an hyperplane of $c$ is isometric
to the whole space if and only if it is $1$complemented. Moreover,
we obtain the classification
of those hyperplanes for which their duals are isometric to
$\ell_{1}$ and we give a complete description of the preduals
of $\ell_{1}$ under the assumption that the standard basis of
$\ell_{1}$
is weak$^{*}$convergent.
Keywords:space of convergent sequences, projection, $\ell_1$predual, hyperplane Categories:46B45, 46B04 

23. CMB 2015 (vol 58 pp. 596)
 Ongaro, Jared; Shapiro, Boris

A Note on Planarity Stratification of Hurwitz Spaces
One can easily show that any meromorphic function
on a complex closed Riemann surface can be represented as a
composition of a birational map of this surface to $\mathbb{CP}^2$ and
a projection of the image curve from an appropriate point
$p\in \mathbb{CP}^2$ to the pencil of lines through $p$. We introduce
a natural stratification of Hurwitz spaces according to the
minimal degree of a plane curve such that a given meromorphic
function can be represented in the above way and calculate the
dimensions of these strata. We observe that they are closely
related to a family of Severi varieties studied earlier by J. Harris,
Z. Ran and I. Tyomkin.
Keywords:Hurwitz spaces, meromorphic functions, Severi varieties 

24. CMB 2015 (vol 58 pp. 271)
25. CMB 2015 (vol 58 pp. 350)
 MerinoCruz, Héctor; Wawrzynczyk, Antoni

On Closed Ideals in a Certain Class of Algebras of Holomorphic Functions
We recently introduced a weighted Banach algebra $\mathfrak{A}_G^n$ of
functions which are holomorphic on the unit disc $\mathbb{D}$, continuous
up to the boundary and of the class $C^{(n)}$ at all points where
the function $G$ does not vanish. Here, $G$ refers to a function
of the disc algebra without zeros on $\mathbb{D}$. Then we proved that
all closed ideals in $\mathfrak{A}_G^n$ with at most countable hull are
standard. In the present paper, on the assumption that $G$ is
an outer function in $C^{(n)}(\overline{\mathbb{D}})$ having infinite roots
in $\mathfrak{A}_G^n$ and countable zero set $h(G)$, we show that all the
closed ideals $I$ with hull containing $h(G)$ are standard.
Keywords:Banach algebra, disc algebra, holomorphic spaces, standard ideal Categories:46J15, 46J20, 30H50 
