Single point extremal functions in Bergman-type spaces
(2002) In Indiana University Mathematics Journal 51(3). p.581-605- Abstract
- Let A be a zero sequence for the Bergman space L-a(2) of the unit disc D, and let phi(A) be the corresponding canoniacal zero divisor. In this paper we consider quotients of the type phi(Au {alpha})/phi(A), alpha is an element of D. By use of methods from the theory of reproducing kernels we shall show that the modulus of such functions is always bounded by 3, and that they can be written as a product of a single Blaschke factor and a function whose real part is greater than 1. Our methods apply in somewhat larger generality. In particular, our results lead to a new proof of the contractive zero-divisor property in weighted Bergman spaces with logarithmically subharmonic weights. For the unweighted Bergman spaces L-a(p), 0 < p <... (More)
- Let A be a zero sequence for the Bergman space L-a(2) of the unit disc D, and let phi(A) be the corresponding canoniacal zero divisor. In this paper we consider quotients of the type phi(Au {alpha})/phi(A), alpha is an element of D. By use of methods from the theory of reproducing kernels we shall show that the modulus of such functions is always bounded by 3, and that they can be written as a product of a single Blaschke factor and a function whose real part is greater than 1. Our methods apply in somewhat larger generality. In particular, our results lead to a new proof of the contractive zero-divisor property in weighted Bergman spaces with logarithmically subharmonic weights. For the unweighted Bergman spaces L-a(p), 0 < p < infinity, we show that the canonical zero divisor phi(A) for a zero sequence with n elements can be written as a product of n starlike functions. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/333305
- author
- Aleman, Alexandru LU and Richter, S
- organization
- publishing date
- 2002
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Bergman spaces, contractive divisors
- in
- Indiana University Mathematics Journal
- volume
- 51
- issue
- 3
- pages
- 581 - 605
- publisher
- Indiana University
- external identifiers
-
- wos:000176918700003
- scopus:0036059736
- ISSN
- 0022-2518
- DOI
- 10.1512/iumj.2002.51.2190
- language
- English
- LU publication?
- yes
- id
- b40a0935-9ab9-4935-99a5-ea4ce359480c (old id 333305)
- date added to LUP
- 2016-04-01 12:32:01
- date last changed
- 2022-01-27 06:22:00
@article{b40a0935-9ab9-4935-99a5-ea4ce359480c, abstract = {{Let A be a zero sequence for the Bergman space L-a(2) of the unit disc D, and let phi(A) be the corresponding canoniacal zero divisor. In this paper we consider quotients of the type phi(Au {alpha})/phi(A), alpha is an element of D. By use of methods from the theory of reproducing kernels we shall show that the modulus of such functions is always bounded by 3, and that they can be written as a product of a single Blaschke factor and a function whose real part is greater than 1. Our methods apply in somewhat larger generality. In particular, our results lead to a new proof of the contractive zero-divisor property in weighted Bergman spaces with logarithmically subharmonic weights. For the unweighted Bergman spaces L-a(p), 0 < p < infinity, we show that the canonical zero divisor phi(A) for a zero sequence with n elements can be written as a product of n starlike functions.}}, author = {{Aleman, Alexandru and Richter, S}}, issn = {{0022-2518}}, keywords = {{Bergman spaces; contractive divisors}}, language = {{eng}}, number = {{3}}, pages = {{581--605}}, publisher = {{Indiana University}}, series = {{Indiana University Mathematics Journal}}, title = {{Single point extremal functions in Bergman-type spaces}}, url = {{http://dx.doi.org/10.1512/iumj.2002.51.2190}}, doi = {{10.1512/iumj.2002.51.2190}}, volume = {{51}}, year = {{2002}}, }