On equivalent reformulations of condition derivation closedness

Abstract

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.

arXiv comment22 pages