单位球上Bloch-Orlicz空间上的复合算子(英文)

Composition operators on Bloch-Orlicz type spaces of the unit ball

本文通过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μ-Bloch空间.利用复分析和构造检验函数的方法,本文研究了单位球上Bloch-Orlicz空间上复合算子Cφ的有界性、紧性是和下有界性,得到了复合算子C_φ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.

Using Young＇ s functions, we aeLm 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 compo- sition operator φ on Bloch-Orlicz type spaces of the unit ball. And we also obtain the sufficient and nec- essary conditions of boundedness.compactness and boundedness from below of the composition operator φ.