Blaschke products with derivative in function spaces

2010/01/28 by David Protas, Protas, David
Mathematics · #30H10 #30H20 #30J10 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1001.5098

openalex publication_date 2010/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let B be a Blaschke product with zeros \a_n\. If B' ∈ A^p_α for certain p and α, it is shown that ∑_n (1 - |a_n|)^β < ∞ for appropriate values of β. Also, if \a_n\ is uniformly discrete and if B' ∈ H^p or B' ∈ A^1+p for any p ∈ (0,1), it is shown that ∑_n (1 - |a_n|)^1-p < ∞.

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