The Gleason's problem for some polyharmonic and hyperbolic harmonic function spaces  

作　　者：HU Zhangjian TANG Xiaomin 

机构地区：[1]Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China

出　　处：《Science China Mathematics》2006年第8期1128-1145,共18页中国科学：数学（英文版）

基　　金：This work is partially supported by the National Natural Science Foundation of China(Grant No.10471039);the Natural Science Foundation of Zhejiang Province(Grant No.M103104).The authors thank the referee for his(her)valuable suggestion.

摘　　要：Let Ω(∈) Rn be a bounded convex domain with C2 boundary. For 0 ＜ p,q ≤∞ and a normal weight ψ, the mixed norm space Hp,q,ψk,(Ω) consists of all polyharmonic functions f of order k for which the mixed norm ||·||p,q,ψ＜∞.In this paper, we prove that the Gleason's problem (Ω,a,Hp,q,ψk) is always solvable for any reference point a ∈Ω. Also, the Gleason's problem for the polyharmonic ψ-Bloch (little ψ-Bloch) space is solvable. The parallel results for the hyperbolic harmonic mixed norm space are obtained.LetΩ Rn be a bounded convex domain with C2 boundary. For 0<p,q≤∞and a normal weightψ. the mixed norm space Hp,q,ψk(Ω) consists of all polyharmonic functions f of order k for which the mixed norm‖·‖p,q,ψ<∞. In this paper, we prove that the Gleason's problem (Ω, a,Hp,q,ψk) is always solvable for any reference point a∈Ω. Also, the Gleason's problem for the polyharmonicψ-Bloch (littleψ-Bloch) space is solvable. The parallel results for the hyperbolic harmonic mixed norm space are obtained.

关 键 词：Gleason's problem  mixed NORM space  Bloch-type space. 

分 类 号：N[自然科学总论]