On Dirichlet spaces with zero sets containing all Blaschke sequences
Abstract
Abstract We consider the family of infinite positive Borel measures μ $\mu $ mu in the unit disc, with finite degree of contact at the unit circle, and the set E μ $E_{\mu }$ upper E Subscript mu of points in the unit circle for which every neighborhood contains infinite mass of μ $\mu $ mu . Assuming that E μ $E_{\mu }$ upper E Subscript mu is a Carleson set, we show that all Blaschke sequences are zero sets for the corresponding Dirichlet space D μ $D_{\mu }$ upper D Subscript mu .
Fields of Study & Subjects
Holomorphic and Operator Theory
Advanced Harmonic Analysis Research
Advanced Banach Space Theory
Publication details
- Journal / source
- Canadian Mathematical Bulletin
- Volume
- 69
- Issue
- 3
- Pages
- 1035–1042
- Publication date
- 14 January 2026
- Language
- EN