Blaschke products with derivative in function spaces
David Protas

TL;DR
This paper investigates the relationship between the derivatives of Blaschke products and the distribution of their zeros within specific function spaces, establishing conditions for zero sequences based on derivative integrability.
Contribution
It provides new criteria linking the integrability of a Blaschke product's derivative to the summability of its zeros' distances from the boundary.
Findings
If B' in A^p_{α}, then sum of (1 - |a_n|)^β converges.
If zeros are uniformly discrete and B' in H^p or A^{1+p}, then sum of (1 - |a_n|)^{1-p} converges.
Derived conditions connect derivative space membership to zero distribution.
Abstract
Let be a Blaschke product with zeros . If for certain and , it is shown that for appropriate values of . Also, if is uniformly discrete and if or for any , it is shown that .
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Banach Space Theory · Advanced Harmonic Analysis Research
