C^n中多圆柱上广义Bloch空间的点乘子

Pointwise multipliers of generalized Bloch space on the multi-circular cylinder domain of C^n

讨论了Cn(n>1)中多圆柱上广义Bloch空间βp上的点乘子,根据p、q的不同情况得到βp空间到βq空间所有的点乘子,得到(1)当p<1时M(βp)=βp;(2)当p≥1时M(βp)=○c;(3)当p>q时M(βp,βq)={0};(4)当p<q<1时M(βp,βq)=βq;(5)当p<1≤q时M(βp,βq)=Jp,q∩βq;(6)当1≤p<q时M(βp,βq)=○c.

The pointwise multipliers of generalized Bloch space on the multi\|circular cylinder domain of Cn are discussed and the pointwise multipliers between βp and βq in different cases about p,q are characterized.It is obtained that (1)if p<1,M(βp)=βp, (2)if p≥1,M(βp)=○c, (3)if p>q,M(βp,βq)={0}, (4)if p<q<1,M(βp,βq)=βq, (5)if p<1≤q,M(βp,βq)=Jp,q∩βq, (6)if 1≤p<q,M(βp,βq)=○c.