On the Membership in Bergman Spaces of the Derivative of a Blaschke Product With Zeros in a Stolz Domain
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Bibliographic record
Abstract
Abstract It is known that the derivative of a Blaschke product whose zero sequence lies in a Stolz angle belongs to all the Bergman spaces A p with 0 < p < 3/2. The question of whether this result is best possible remained open. In this paper, for a large class of Blaschke products B with zeros in a Stolz angle, we obtain a number of conditions which are equivalent to the membership of B ′ in the space A p ( p < 1). As a consequence, we prove that there exists a Blaschke product B with zeros on a radius such that B ′ ∉ A 3/2 .
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Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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