# Journal of Operator Theory

Volume 74, Issue 1, Summer 2015 pp. 149-175.

Constructing Frostman-Blaschke products and
applications to operators on weighted Bergman spaces

**Authors**:
John R. Akeroyd (1)
and Pamela Gorkin (2)

**Author institution:**(1) Department of Mathematics, University of Arkansas,
Fayetteville, AR 72701, U.S.A.

(2) Department of Mathematics, Bucknell University, Lewisburg, PA, 17837,
U.S.A.

**Summary: **We give an example of a uniform Frostman--Blaschke
product $B$, whose spectrum is a Cantor set, such that
the composition operator $C_B$ is not closed-range on any weighted Bergman
space $\mathbb{A}_{\alpha}^p$, answering two
questions posed in recent papers. We include some general observations about
these Blaschke products. Using methods
developed in our first example, we improve upon a theorem of V.I. Vasjunin
concerning the rate at which the zeros of a uniform
Frostman--Blaschke product approach the unit circle.

**DOI: **http://dx.doi.org/10.7900/jot.2014may14.2026

**Keywords: **Bergman space, Frostman-Blaschke product, composition
operator, harmonic measure

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