C^n中H~∞空间和小p-Bloch空间之间的乘子

THE FUNCTION MULTIPLIERS BETWEEN LITTLE p-BLOCH SPACE AND H~∞ SPACE OF C^n

函数空间点乘子的刻划对研究函数空间算子理论和函数空间性质有着直接的意义 .本文借助Bergman算子、阶的估计、泛函理论等知识刻划了Hardy空间H∞ 到小p -Bloch空间 βρ0 以及 βρ0 到H∞ 的点乘子 ,得到了完整的乘子空间M(H∞ ,βρ0 )和M(β ρ0 ,H∞) ,即 (i) 0 ≤p <1时 ,φ∈M(H∞ ,βρ0 ) φ≡ 0 ; p >1时 ,M(H∞ ,βρ0 ) =βρ0 ; p≥ 1时 ,φ ∈M(βρ0 ,H∞) φ≡ 0 ; 0 <p<1时 ,M(βρ0 ,H∞) =H∞ .

To characterize the pointwise multiplier of function space has the direct meaning to study the operator theory and property of function space.The pointwise multipliers from Hardy space H ∞ to little p-Bloch space β p 0 and from β p 0 to H ∞ were characterized by using Bergman operator,estimation of order,functional theory etc.And the complete multiplier spaces M(H ∞,β ρ 0 ) and M(β ρ 0 .H ∞) were obtained,that is ? if 0≤p<1,then φ∈M(H ∞,β ρ 0 )φ≡0;? if p>1,then M(H ∞,β ρ 0 )=β ρ 0 ;? if p≥1,then φ∈M(β ρ 0 ,H ∞)φ≡0;? if 0<p<1 M(β ρ 0 ,H ∞)=H ∞.