Single point extremal functions in Bergmantype spaces
(2002) In Indiana University Mathematics Journal 51(3). p.581605 Abstract
 Let A be a zero sequence for the Bergman space La(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 zerodivisor property in weighted Bergman spaces with logarithmically subharmonic weights. For the unweighted Bergman spaces La(p), 0 < p <... (More)
 Let A be a zero sequence for the Bergman space La(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 zerodivisor property in weighted Bergman spaces with logarithmically subharmonic weights. For the unweighted Bergman spaces La(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
 00222518
 DOI
 10.1512/iumj.2002.51.2190
 language
 English
 LU publication?
 yes
 id
 b40a09359ab9493599a5ea4ce359480c (old id 333305)
 date added to LUP
 20160401 12:32:01
 date last changed
 20200112 10:00:23
@article{b40a09359ab9493599a5ea4ce359480c, abstract = {Let A be a zero sequence for the Bergman space La(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 zerodivisor property in weighted Bergman spaces with logarithmically subharmonic weights. For the unweighted Bergman spaces La(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 = {00222518}, language = {eng}, number = {3}, pages = {581605}, publisher = {Indiana University}, series = {Indiana University Mathematics Journal}, title = {Single point extremal functions in Bergmantype spaces}, url = {http://dx.doi.org/10.1512/iumj.2002.51.2190}, doi = {10.1512/iumj.2002.51.2190}, volume = {51}, year = {2002}, }