Bergman空间和Zygmund空间之间的广义Cesàro算子

Extended Cesro Operators Between Bergman Spaces and Zygmund Spaces

通过引入试验函数的方法,一方面给出了Bergman到￡空间的映射Tg为有界算子(或紧算子)的充要条件是g≡C;另一方面得到了￡空间到Bergman空间的映射Tg为有界算子(或紧算子)的充要条件是g∈Apα.此处g是一个给定的全纯函数,(Tgf)(z)

By making use of test function, we obtain extended Ces ro operators Tg from the Bergman space Aa^p to the Zygmund space ￡ that is bounded（or compact） if and only if g≡C, and on the other hand, we extend Cesaro operators Tg from Zygmund space ￡ to the Bergman space Aa^p that is bounded （or compact） if and only if g ∈Aa^p ,where g is a given holomorphic function on the open unit disk D and Tg is defined by （Tgf）（z）=∫0^z（ξ）dξ.