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Estimates in Möbius invariant spaces of analytic functions.

Aleman, Alexandru LU and Persson, Anna-Maria LU (2004) In Complex Variables, Theory & Application 49(7-9). p.487-510
Abstract
We consider a class of spaces of analytic functions on the unit disc which are Möbius invariant and whose topology is essentially determined by a conformal invariant seminorm. Standard examples of such spaces are the Bloch space. BMOA, the Dirichlet spaces and their recent generalizations ${Cal Q}_K$, which make the object of our interest. We prove a general inequality for the seminorms of dilated functions, radial growth estimates, embedding theorems in $L^p$-spaces on the unit disc, as well as integral estimates of exponentials of functions in such spaces. Finally, we discuss some properties of the inner-outer factorization for those ${Cal Q}_K$ spaces which are contained in the Nevanlinna class.
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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Complex Variables, Theory & Application
volume
49
issue
7-9
pages
487 - 510
publisher
New York ; Gordon and Breach, 1982-
ISSN
1563-5066
language
English
LU publication?
yes
id
6a6d63d3-f3e3-48e6-8fd7-1bfab359f627 (old id 791167)
date added to LUP
2016-04-04 07:29:01
date last changed
2018-11-21 20:48:32
@article{6a6d63d3-f3e3-48e6-8fd7-1bfab359f627,
  abstract     = {{We consider a class of spaces of analytic functions on the unit disc which are Möbius invariant and whose topology is essentially determined by a conformal invariant seminorm. Standard examples of such spaces are the Bloch space. BMOA, the Dirichlet spaces and their recent generalizations ${Cal Q}_K$, which make the object of our interest. We prove a general inequality for the seminorms of dilated functions, radial growth estimates, embedding theorems in $L^p$-spaces on the unit disc, as well as integral estimates of exponentials of functions in such spaces. Finally, we discuss some properties of the inner-outer factorization for those ${Cal Q}_K$ spaces which are contained in the Nevanlinna class.}},
  author       = {{Aleman, Alexandru and Persson, Anna-Maria}},
  issn         = {{1563-5066}},
  language     = {{eng}},
  number       = {{7-9}},
  pages        = {{487--510}},
  publisher    = {{New York ; Gordon and Breach, 1982-}},
  series       = {{Complex Variables, Theory & Application}},
  title        = {{Estimates in Möbius invariant spaces of analytic functions.}},
  volume       = {{49}},
  year         = {{2004}},
}