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Invariant subspaces with finite codimension in Bergman spaces

Aleman, Alexandru LU (1992) In Transactions of the American Mathematical Society 330(2). p.531-544
Abstract
Let $\Omega$ be a domain in the complex plane. Denote by $L^p_{\roman{a}}(\Omega)$ $(1\le p<+\infty)$ the Bergman space over $\Omega$. The author presents a description of finite codimensional space $E\subset L^p_{\roman{a}}(\Omega)$ such that $zE\subset E$. Under some conditions on $\Omega$ an analogous result is due to \n S. Axler\en and \n P. Bourdon\en [same journal {\bf306} (1988), no. 2, 805--817; MR0933319 (89f:46051)].



For an arbitrary bounded domain in C there are described those finite codimensional subspaces of the Bergman space that are invariant under multiplication by z.
Please use this url to cite or link to this publication:
author
publishing date
type
Contribution to journal
publication status
published
subject
in
Transactions of the American Mathematical Society
volume
330
issue
2
pages
531 - 544
publisher
American Mathematical Society (AMS)
external identifiers
  • scopus:84966253530
ISSN
0002-9947
language
English
LU publication?
no
id
8d2c2fc7-8c32-4ad0-ad07-f11832f31dd1 (old id 1467372)
alternative location
http://www.jstor.org/stable/pdfplus/2153921.pdf
date added to LUP
2016-04-01 16:09:19
date last changed
2021-01-03 06:17:32
@article{8d2c2fc7-8c32-4ad0-ad07-f11832f31dd1,
  abstract     = {{Let $\Omega$ be a domain in the complex plane. Denote by $L^p_{\roman{a}}(\Omega)$ $(1\le p&lt;+\infty)$ the Bergman space over $\Omega$. The author presents a description of finite codimensional space $E\subset L^p_{\roman{a}}(\Omega)$ such that $zE\subset E$. Under some conditions on $\Omega$ an analogous result is due to \n S. Axler\en and \n P. Bourdon\en [same journal {\bf306} (1988), no. 2, 805--817; MR0933319 (89f:46051)].<br/><br>
<br/><br>
For an arbitrary bounded domain in C there are described those finite codimensional subspaces of the Bergman space that are invariant under multiplication by z.}},
  author       = {{Aleman, Alexandru}},
  issn         = {{0002-9947}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{531--544}},
  publisher    = {{American Mathematical Society (AMS)}},
  series       = {{Transactions of the American Mathematical Society}},
  title        = {{Invariant subspaces with finite codimension in Bergman spaces}},
  url          = {{http://www.jstor.org/stable/pdfplus/2153921.pdf}},
  volume       = {{330}},
  year         = {{1992}},
}