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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
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
2007-12-27 13:17:26
date last changed
2016-04-16 05:44:10
@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},
}