Volterra型算子在对数加权Banach空间之间的有界性和紧性

The Boundedness and Compactness of Volterra Type Operators Between Logarithm-Weighted Banach Spaces

Smith等人近年来给出了当符号函数为单叶函数时,Volterra型算子在有界解析函数Banach空间上的有界性的充要条件.本文在其基础上,刻画了Volterra型算子T_g在对数加权Banach空间之间的有界性和紧性的充要条件,从而扩展了他们的成果.最后提出一些未解问题.

Smith et al. recently gave the sufficient and necessary conditions for the boundedness of Volterra type operators on Banach spaces of bounded analytic functions when the symbol functions are univalent. In this paper, following their ideas,we characterize the conditions for the boundedness and compactness of Volterra type operators T_g between logarithm-weighted Banach spaces of analytic functions, which extend their works. Finally, some unsolved problems are posed.