Abstract view
A Beurling Theorem for Generalized Hardy Spaces on a Multiply Connected Domain


Yanni Chen,
School of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710119, China
Don Hadwin,
Department of Mathematics, University of New Hampshire, Durham, NH 03824, USA
Zhe Liu,
Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA
Eric Nordgren,
Department of Mathematics, University of New Hampshire, Durham, NH 03824, USA
Abstract
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
Beurling theorem, invariant subspace, generalized Hardy space, gauge norm, multiply connected domain, Forelli projection, innerouter factorization, affiliated operator
