Zygmund空间上的微分复合算子

Composition Followed by Differentiation on the Zygmund Space

讨论Zygmund空间E={f∈H（D）：sup_（z∈D）（l-｜z｜~2）｜f″（z）｜〈∞}上的微分复合算子DC_φ,这里C_φ是复合算子,D是微分算子.得到了DC_φ在Zygmund空间E和小Zygmund空间E_0上是有界算子与紧算子的充分必要条件.

We consider linear product operator DC_φ acting on the Zygmund space E = {f∈ H（D）：sup_（z∈D）（l-｜z｜~2）｜f＂（z）｜ ∞},where C_φ is the composition operator and D is the differentiation operator.The boundedness and compactness of the operator DC_φ on the Zygmund space E and the little Zygmund space E_0 are estabhshed in terms of the function theorectic property of the symbol φ.