It is shown that on the egg domains: $$\Omega _a = \{ \xi = (z,w) \in {\bf{ }}{\Bbb C}^m ,{\bf{ }}w \in {\bf{ }}{\Bbb C}^m ,{\bf{ }}|z|^2 + |w|^{2/a}< 1\} ,{\bf{ }}0< a \leqslant 2$$ Gleason’s problem can be so...It is shown that on the egg domains: $$\Omega _a = \{ \xi = (z,w) \in {\bf{ }}{\Bbb C}^m ,{\bf{ }}w \in {\bf{ }}{\Bbb C}^m ,{\bf{ }}|z|^2 + |w|^{2/a}< 1\} ,{\bf{ }}0< a \leqslant 2$$ Gleason’s problem can be solved in the weight Bergman space. As an application, multiplier theorem on the egg domains is obtained.展开更多
Necessary and sufficient conditions are obtained for the boundedness of Berezin transformation on Lebesgue space Lp(B,dVβ) in the real unit ball B in Rn. As an application, we prove that Gleason type problem is solva...Necessary and sufficient conditions are obtained for the boundedness of Berezin transformation on Lebesgue space Lp(B,dVβ) in the real unit ball B in Rn. As an application, we prove that Gleason type problem is solvable in hyperbolic harmonic Bergman spaces. Furthermore we investigate the boundary behavior of the solutions of Gleason type problem.展开更多
Let Ω be a bounded convex domain with C2 boundary in C2 and for given 0 < p, q ≤∞ and normal weight function (r) let Hp,q, be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω...Let Ω be a bounded convex domain with C2 boundary in C2 and for given 0 < p, q ≤∞ and normal weight function (r) let Hp,q, be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω, a, Hp,q,) is solvable for any fixed point a ∈ Ω. While solving the Gleason's problem we obtain the boundedness of certain integral operator on Hp,q,.展开更多
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 ||&#...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.展开更多
It is proved that the Bergman type operatorT, is a bounded projection from the pluriharmonic Bergman spaceL p (B)∩h(B) onto Bergman spaceL p (B) ∩ H(B) for 0p 1 ands (p1-1)(n+1). As an application it is shown that t...It is proved that the Bergman type operatorT, is a bounded projection from the pluriharmonic Bergman spaceL p (B)∩h(B) onto Bergman spaceL p (B) ∩ H(B) for 0p 1 ands (p1-1)(n+1). As an application it is shown that the Gleason’s problem can be solved in Bergman space LP(B)∩H(B) for 0p 1.展开更多
文摘It is shown that on the egg domains: $$\Omega _a = \{ \xi = (z,w) \in {\bf{ }}{\Bbb C}^m ,{\bf{ }}w \in {\bf{ }}{\Bbb C}^m ,{\bf{ }}|z|^2 + |w|^{2/a}< 1\} ,{\bf{ }}0< a \leqslant 2$$ Gleason’s problem can be solved in the weight Bergman space. As an application, multiplier theorem on the egg domains is obtained.
基金supported by the National Natural Science Fountation of China(Grant No.10001030)the Post-doctoral Fellowship of University of Aveiro,UI&D"Matematica e Aplicacoes".
文摘Necessary and sufficient conditions are obtained for the boundedness of Berezin transformation on Lebesgue space Lp(B,dVβ) in the real unit ball B in Rn. As an application, we prove that Gleason type problem is solvable in hyperbolic harmonic Bergman spaces. Furthermore we investigate the boundary behavior of the solutions of Gleason type problem.
基金supported by the 151 Projetion and the Natural Science Foundation of Zhejiang Province.
文摘Let Ω be a bounded convex domain with C2 boundary in C2 and for given 0 < p, q ≤∞ and normal weight function (r) let Hp,q, be the mixed norm space on Ω. In this paper we prove that the Gleason's problem (Ω, a, Hp,q,) is solvable for any fixed point a ∈ Ω. While solving the Gleason's problem we obtain the boundedness of certain integral operator on Hp,q,.
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.
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19871081)the Doctoral Program Foundation of the State Education Commission of China
文摘It is proved that the Bergman type operatorT, is a bounded projection from the pluriharmonic Bergman spaceL p (B)∩h(B) onto Bergman spaceL p (B) ∩ H(B) for 0p 1 ands (p1-1)(n+1). As an application it is shown that the Gleason’s problem can be solved in Bergman space LP(B)∩H(B) for 0p 1.
