上半平面的Hardy空间到增长型空间和Bloch空间的加权复合算子

Weighted Composition Operator from Hardy to Growth and Bloch Spaces over Upper Half-plane

讨论了从上半平面的H ardy空间Hp(Π+)到增长型空间A∞(Π+)和B loch空间B∞(Π+)的加权复合算子的有界性,得到以下结论:(i)uCφ是空间Hp(Π+)到A∞(Π+)之间的有界算子的充要条件;(ii)uCφ是空间Hp(Π+)到B∞(Π+)之间的有界算子的充要条件.

The boundedness of the weighted composition operator uCφ from Hardy spaces Hp（Π＋） to growth spaces A∞（Π＋） and Bloch spaces B∞（Π＋） over the upper half-plane is researched.It is obtained as follows：（i）some necessary and sufficient conditions are given for which uCφ is a bounded operator from Hp（Π＋） to A∞（Π＋）;（ii） some necessary and sufficient conditions are given for which uCφ is a bounded operator from Hp（Π＋） to B∞（Π＋）.