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Estimates in Möbius invariant spaces of analytic functions.

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Author

Summary, in English

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.

Publishing year

2004

Language

English

Pages

487-510

Publication/Series

Complex Variables, Theory & Application

Volume

49

Issue

7-9

Document type

Journal article

Publisher

New York ; Gordon and Breach, 1982-

Topic

  • Mathematics

Status

Published

ISBN/ISSN/Other

  • ISSN: 1563-5066