单位球上Bloch-Orlicz空间上的复合算子

Composition operators on Bloch-Orlicz type Spaces of the unit Ball

摘要:

通过Young函数定义了Bloch-Orlicz空间, 得出该空间等距同构于一类特殊的 -Bloch空间. 利用复分析和构造检验函数的方法, 研究了单位球上Bloch-Orlicz空间上复合算子的有界性、紧性是和下有界性, 得到了复合算子是Bloch-Orlicz空间上的有界算子、紧性算子和下有界算子的充要条件.

Abstract:

Using Young’s functions, we define the Bloch-Orlicz space and show that the Bloch-Orlicz space is isometrically equal to a special certain -Bloch space. By the analysis methods and constructing test functions, we investigate the boundedness, compactness and boundedness from below of the composition operator on Bloch-Orlicz type spaces of the unit ball, and obtain the sufficient and necessary conditions of boundedness、compactness and boundedness from below of the composition operator.