Single point extremal functions in Bergman-type spaces

Alexandru Aleman, S Richter

Research output: Contribution to journalArticlepeer-review

3 Citations (SciVal)

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.
Original languageEnglish
Pages (from-to)581-605
JournalIndiana University Mathematics Journal
Volume51
Issue number3
DOIs
Publication statusPublished - 2002

Subject classification (UKÄ)

  • Mathematics

Keywords

  • Bergman spaces
  • contractive divisors

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