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Single point extremal functions in Bergman-type spaces

In English

Författare

Summary, in English

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.

Publiceringsår

2002

Språk

Engelska

Sidor

581-605

Publikation/Tidskrift/Serie

Indiana University Mathematics Journal

Volym

51

Issue

3

Dokumenttyp

Artikel i tidskrift

Förlag

Indiana University

Ämne

  • Mathematics

Nyckelord

  • Bergman spaces
  • contractive divisors

Status

Published

ISBN/ISSN/Övrigt

  • ISSN: 0022-2518