Hypercyclic linear fractional composition operators on weighted Dirichlet spaces D-alpha(p)
Hypercyclic linear fractional composition operators on weighted Dirichlet spaces D-alpha(p)
复制标题
加权狄利克雷空间上的超循环线性分数复合算子 D-alpha(p)
DOI：
10.1016/j.jmaa.2018.12.033
复制
发表时间：
2019
影响因子：
1.3
通讯作者：
Shu Yonglu
中科院分区：
文献类型：
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作者：
Guo Zhitao;Shu Yonglu
摘要最近，F.科隆纳和RA Martínez-Avendaño提出了当p− 2< α<p时加权Dirichlet空间D α p是否支持超循环复合算子的问题，本文研究了D α p上复合算子的超循环性，部分回答了这个问题.特别地，在假设p− 2< α< p的条件下，我们证明了由单位圆盘的抛物自同构或双曲自同构诱导的复合算子在D α p上是超循环的，如果p> 3。此外，由双曲非自同构诱导的复合算子在D α p上是超循环的，对所有p> 1且p− 1< α<p。
Abstract Recently, F. Colonna and RA Martínez-Avendaño raised the open question that whether or not the weighted Dirichlet spaces D α p can support hypercyclic composition operators when p− 2< α< p. In this paper, we investigate the hypercyclicity of composition operators on D α p and partially answer the question. Specifically, under the assumption p− 2< α< p, we show that the composition operator induced by a parabolic automorphism or a hyperbolic automorphism of the unit disk is hypercyclic on D α p if p> 3. Furthermore, the composition operator induced by a hyperbolic non automorphism is hypercyclic on D α p for all p> 1 and p− 1< α< p.