In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not pre...In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.展开更多
若D为Reinhardt域 D={Z∈C^n:‖z‖_α=sum from j=1 to n(|z_j|^(2/α_j)<1)},这里0<α_j,j=1,2,…,n。证明了:若K_D(z,)为D的Bergman核函数,则存在两个正的常数m与M,不依赖于z,而只依赖于α=(α_1,…,α_n)及n,使得 mF(z,)≤K_D...若D为Reinhardt域 D={Z∈C^n:‖z‖_α=sum from j=1 to n(|z_j|^(2/α_j)<1)},这里0<α_j,j=1,2,…,n。证明了:若K_D(z,)为D的Bergman核函数,则存在两个正的常数m与M,不依赖于z,而只依赖于α=(α_1,…,α_n)及n,使得 mF(z,)≤K_D(z,)≤MF(z,z)对任一z∈D都成立,这里 F(z,)=(-r(z))^(-n-1) multiply from j=1 to n ((-r(z)+|z_j|^(2/α_j))^(1-α_j)),而r(z)=‖z‖_α-1为D的定义函数。展开更多
文摘In this paper, we introduce the generalized R oper-Suffridge extension operator for locally biholomorphic mappings. It is sh own that this operator preserves the starlikeness on some Reinhardt domains and does not preserve convexity for some cases. Meanwhile, the growth theorem and di stortion theorem of the corresponding mappings are given.
文摘若D为Reinhardt域 D={Z∈C^n:‖z‖_α=sum from j=1 to n(|z_j|^(2/α_j)<1)},这里0<α_j,j=1,2,…,n。证明了:若K_D(z,)为D的Bergman核函数,则存在两个正的常数m与M,不依赖于z,而只依赖于α=(α_1,…,α_n)及n,使得 mF(z,)≤K_D(z,)≤MF(z,z)对任一z∈D都成立,这里 F(z,)=(-r(z))^(-n-1) multiply from j=1 to n ((-r(z)+|z_j|^(2/α_j))^(1-α_j)),而r(z)=‖z‖_α-1为D的定义函数。
