对数(α,β)-Bloch空间的新刻画

New Characterizations of Logarithmic(α,β)-Bloch Spaces

讨论了单位圆盘上对数(α,β)-Bloch空间的积分性质,得到了该空间的五个等价刻画.并对小对数(α,β)-Bloch空间做了类似推广,得到了小对数(α,β)-Bloch空间的五个等价刻画.最后,利用Carleson测度这个重要工具对这两个空间进行了描述,得到了解析函数分别属于这两个空间的充分条件.

In this paper,the integral property of logarithmic（α,β）-Bloch spaces on the unit disk is discussed and five characterizations are given. The similar conclusions to little logarithmic（α,β）-Bloch spaces are extended,and five characterizations are obtained.Finally,Carleson measure is used to describe the above two spaces. Some sufficient conditions for which analytic functions are in the two spaces,respectively,are given.