Journal d'Analyse Mathématique

, Volume 103, Issue 1, pp 307–329

Uniqueness theorems for Korenblum type spaces


DOI: 10.1007/s11854-008-0010-z

Cite this article as:
Borichev, A. & Lyubarskii, Y. J Anal Math (2007) 103: 307. doi:10.1007/s11854-008-0010-z


For a scale of spaces X of functions analytic in the unit disc, including the Korenblum space, and for some natural families ɛ of uniqueness subsets for X, we describe minorants for (X, ɛ), that is, non-decreasing functions M: (0, 1) → (0, ∞) such that fX, E ∈ ɛ, and log |f(z)| ≤ −M(|z|) on E imply f = 0. We give an application of this result to approximation by simple fractions with restrictions on the coefficients.

Copyright information

© The Hebrew University of Jerusalem 2007

Authors and Affiliations

  1. 1.Centre de Mathématiques et InformatiqueUniversité d’Aix-Marseille IMarseilleFrance
  2. 2.Department of Mathematical SciencesNorwegian University of Science and TechnologyTrondheimNorway