Factorization of Functions in Weighted Bergman Spaces

Charles Horowitz; Yehudah Schnaps

Factorization of Functions in Weighted Bergman Spaces

Charles Horowitz, Yehudah Schnaps

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We consider spaces A^p,φ of analytic functions on the unit disc which are in L^p with respect to a measure of the form φ(r)drdθ, where φ is "submultiplicative". We show that these spaces are Möbius invariant and that if f ∈ A^p,φ one can factor out some or all of its zeros in a standard bounded way; also one can represent f as a product of two functions in A²^p,φ. Finally, we show that our methods cannot be extended to the case of φ not submultiplicative.

Original language	English
Pages (from-to)	891-903
Number of pages	13
Journal	Annali della Scuola normale superiore di Pisa - Classe di scienze
Volume	29
Issue number	4
State	Published - 2000
Externally published	Yes

Bibliographical note

Publisher Copyright:
© Scuola Normale Superiore, Pisa, 2000, tous droits réservés.

Cite this

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Factorization of Functions in Weighted Bergman Spaces

Abstract

Bibliographical note

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