Weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces
Weighted differentiation composition operators from mixed-norm spaces to weighted-type spaces
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DOI：
10.1016/j.amc.2009.01.061
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发表时间：
2009-05
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影响因子：
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通讯作者：
S. Stević
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文献类型：
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作者：
S. Stević
受最近的论文[X.]从Bergman型空间到Bers型空间的微分、组合与乘法积，积分变换。Spec. Funct. 18(3)(2007) 223-231]，研究了加权微分复合算子Dφ，un(f)(z)=u(z)f(n)（φ(z)）的有界性和紧性，其中u是单位盘D上的全纯函数，φ是D和n∈N0的全纯自映射，从混合范数空间H(p,q, φ)，其中p，q>0和φ是正规的，到加权型空间Hμ，0∞或小加权型空间Hμ，0∞。对于加权Bergman空间Aαp， p>1，给出了算子本质范数的一些界。
Motivated by the recent paper [X. Zhu, Products of differentiation composition and multiplication from Bergman type spaces to Bers spaces, Integral Transform. Spec. Funct. 18 (3) (2007) 223–231], we study the boundedness and compactness of the weighted differentiation composition operator Dφ,un(f)(z)=u(z)f(n)(φ(z)), where u is a holomorphic function on the unit disk D, φ is a holomorphic self-map of D and n∈N0, from the mixed-norm space H(p,q,ϕ), where p,q>0 and ϕ is normal, to the weighted-type space Hμ∞or the little weighted-type space Hμ,0∞. For the case of the weighted Bergman space Aαp, p>1, some bounds for the essential norm of the operator are also given.