发表机构
Universität Wien（维也纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文系统研究权重序列条件推导封闭性的等价形式，指出其保证加权空间导数稳定性，并构造反例说明缺少对数凸性时完整刻画失效。
AI 中文摘要
我们详细研究了权重序列经典条件推导封闭性的等价重述。该性质在许多应用中至关重要，因为它确保相应的加权空间满足在取导数下的稳定性这一期望性质。此外，它产生各种方向和证明所需的技术估计，因此了解不同条件等价于这一关键要求在处理加权空间时是重要且有用的。最后，我们构造了一个明确的（反）例子，表明在没有标准条件对数凸性时，完整刻画通常失败，并讨论了混合情形。
英文摘要
We provide a detailed study of equivalent reformulations of the classical condition derivation closedness for weight sequences. This property is crucial in many applications since it ensures that the corresponding weighted spaces satisfy the desired property of stability under taking derivatives. Moreover, it yields technical estimates which are required in various directions and proofs and so the knowledge that different conditions are equivalent to this crucial requirement is important and useful when dealing with weighted spaces. Finally, we construct an explicit (counter-)example which shows that without the standard condition log-convexity the full characterization fails in general and comment on the mixed setting as well.
Comments22 pages
