关于复平面上H∞空间,βp空间以及β0p空间的几个问题

Remarks on Spaces H∞, βp, and β0p on Complex Plane

中文关键词:  有界性  加权复合算子  点乘子  紧算子

英文关键词:boundedness  weighted composition operator  pointwise multiplier  compact operator.

中文摘要:

      本文讨论了单位圆中Hardy空间H^∞到p-Bloch空间β^p的复合算子T_1,φ加权复合算子T_ψ,φ的有界性,也讨论了H^∞到小p-Bloch空间β₀^p的复合算子T_1,φ的有界性问题;另外还讨论了小p-Bloch空间到H^∞空间的点乘子及小p-Bloch空间上复合算子的紧性等.

英文摘要:

      In this paper, we discuss the boundedness of the composition operator T_1,φ and weighted composition operator T_ψ,φ from Hardy space H^∞ to p-Bloch space β^p on the unit disc, and obtain the sufficient and necessary condition. We study the pointwise multipliers from space β₀^p to H^∞ on the unit disc and the compactness of T_1,φ from space β₀^p to β₀^q. We consider the boundedness of the composition operator T_1,φ from H^∞ to little p-Bloch space, and obtain the sufficient and necessary condition.