IUMJ

Title: Majorants of meromophic functions with fixed poles

Authors: A. D. Baranov, A. A. Borichev and V. P. Havin

Issue: Volume 56 (2007), Issue 4, 1595-1628

Abstract:

Let $B$ be a meromorphic Blaschke product in the upper half-plane with zeros $z_n$ and let $K_B = H^2 \ominus BH^2$ be the associated model subspace of the Hardy space $H^2$. A nonnegative function $w$ on the real line is said to be an admissible majorant for $K_B$ if there is a non-zero function $f \in K_B$ such that $|f| \le w$ a.e. on $\mathbb{R}$. We study the relations between the distribution of the zeros of a Blaschke product $B$ and the class of admissible majorants for the space $K_B$.