Suppose that φ is an analytic self-map of the unit disk Δ. We consider compactness of the composition operator Cφ from the Bloch space B into the spaces QK defined by a nonnegative, nondecreasing function K（r） f...Suppose that φ is an analytic self-map of the unit disk Δ. We consider compactness of the composition operator Cφ from the Bloch space B into the spaces QK defined by a nonnegative, nondecreasing function K（r） for 0 ≤ r 〈 Cφ. Our compactness condition depends only on Φ which can be considered as a slight improvement of the known results. The compactness of Cφ from the Dirichlet space D into the spaces QK is also investigated,展开更多
在文献[1]中,Sharma A K讨论了Bergman空间Bloch型空间六种算子M_ψC_φD、M_ψDC_φ、C_φM_ψD、DM_ψC_φ、C_φDM_ψ、DC_φM_ψ.受此启发,本文研究Q_K(p,q)空间到Bloch型空间上的Stevi?-Sharma算子的有界性和紧性,并给出了当p≠q+2...在文献[1]中,Sharma A K讨论了Bergman空间Bloch型空间六种算子M_ψC_φD、M_ψDC_φ、C_φM_ψD、DM_ψC_φ、C_φDM_ψ、DC_φM_ψ.受此启发,本文研究Q_K(p,q)空间到Bloch型空间上的Stevi?-Sharma算子的有界性和紧性,并给出了当p≠q+2时Q_K(p,q)空间到Bloch型空间上的Stevi?-Sharma算子是有界算子或紧算子的充分必要条件.本文的结果推广了文献[2,3]中的部分结果.展开更多
基金the National Natural Science Foundation of China (No.10371069) and the NSF of Guangdong Province of China (No.04011000)
文摘Suppose that φ is an analytic self-map of the unit disk Δ. We consider compactness of the composition operator Cφ from the Bloch space B into the spaces QK defined by a nonnegative, nondecreasing function K（r） for 0 ≤ r 〈 Cφ. Our compactness condition depends only on Φ which can be considered as a slight improvement of the known results. The compactness of Cφ from the Dirichlet space D into the spaces QK is also investigated,
基金Supported by the National Natural Science Foundation of China(10671147)Science Foundation of Ministry of Education of China(208081)the Natural Science Foundation of Henan(2008B110006)
基金the Natural Science Foundation of China(10471039)the Higher Schools Natural Science Basic Research Foundation of Jiangsu Province(06KJD11017507KJB110115)
文摘在文献[1]中,Sharma A K讨论了Bergman空间Bloch型空间六种算子M_ψC_φD、M_ψDC_φ、C_φM_ψD、DM_ψC_φ、C_φDM_ψ、DC_φM_ψ.受此启发,本文研究Q_K(p,q)空间到Bloch型空间上的Stevi?-Sharma算子的有界性和紧性,并给出了当p≠q+2时Q_K(p,q)空间到Bloch型空间上的Stevi?-Sharma算子是有界算子或紧算子的充分必要条件.本文的结果推广了文献[2,3]中的部分结果.
