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

Abstract:

      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.