1. CJM Online first
 Chen, Yanni; Hadwin, Don; Liu, Zhe; Nordgren, Eric

A Beurling Theorem for Generalized Hardy Spaces on a Multiply Connected Domain
The object of this paper is to prove a version of the BeurlingHelsonLowdenslager
invariant subspace theorem for operators on certain Banach spaces
of functions on a multiply connected domain in $\mathbb{C}$. The norms
for these spaces are either the usual Lebesgue and Hardy space
norms or certain continuous gauge norms.
In the Hardy space case the expected corollaries include the
characterization of the cyclic vectors as the outer functions
in this context, a demonstration that the set of analytic multiplication
operators is maximal abelian and reflexive, and a determination
of the closed operators that commute with all analytic multiplication
operators.
Keywords:Beurling theorem, invariant subspace, generalized Hardy space, gauge norm, multiply connected domain, Forelli projection, innerouter factorization, affiliated operator Categories:47L10, 30H10 

2. CJM Online first
 Bao, Guanlong; Göğüş, Nihat Gökhan; Pouliasis, Stamatis

On Dirichlet spaces with a class of superharmonic weights
In this paper, we investigate Dirichlet spaces $\mathcal{D}_\mu$ with
superharmonic weights induced by positive Borel measures $\mu$
on
the open unit disk. We establish the AlexanderTaylorUllman
inequality for $\mathcal{D}_\mu$ spaces and we characterize the cases where
equality occurs.
We define a class of weighted Hardy spaces $H_{\mu}^{2}$ via
the balayage of the measure $\mu$.
We show that $\mathcal{D}_\mu$
is equal to $H_{\mu}^{2}$ if and only if $\mu$ is a
Carleson measure for $\mathcal{D}_\mu$. As an application, we obtain the
reproducing kernel of $\mathcal{D}_\mu$ when $\mu$ is an infinite
sum of point mass measures. We consider the boundary
behavior and innerouter factorization of functions in $\mathcal{D}_\mu$.
We also characterize the boundedness and
compactness of composition operators on $\mathcal{D}_\mu$.
Keywords:Dirichlet space, Hardy space, superharmonic weight Categories:30H10, 31C25, 46E15 

3. CJM Online first
 Fricain, Emmanuel; Rupam, Rishika

On asymptotically orthonormal sequences
An asymptotically orthonormal sequence is a sequence which is
"nearly" orthonormal in the sense that it satisfies the Parseval
equality up to two constants close to one. In this paper, we
explore such sequences formed by normalized reproducing kernels
for model spaces and de BrangesRovnyak spaces.
Keywords:function space, de BrangesRovnyak and model space, reproducing kernel, asymptotically orthonormal sequence Categories:30J05, 30H10, 46E22 

4. CJM 2011 (vol 64 pp. 1329)