The Gleasons problem for some polyharmonic and hyperbolic harmonic function spaces

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.

作 者： HU Zhangjian TANG Xiaomin   作者單位： Department of Mathematics, Huzhou Teachers College, Huzhou 313000, China  刊 名： 中國科學A輯（英文版）  SCI 英文刊名： SCIENCE IN CHINA (MATHEMATICS)  年，卷(期)： 2006 49(8)  分類號： O1  關鍵詞： Gleason's problem   mixed norm space   Bloch-type space  

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