Estimates in Möbius invariant spaces of analytic functions.
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/791167
- author
- Aleman, Alexandru LU and Persson, Anna-Maria LU
- organization
- publishing date
- 2004
- 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}}, }