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论文类型：期刊论文

发表时间：2018-04-01

发表刊物：BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY

收录刊物：SCIE、Scopus

卷号：97

期号：2

页面范围：297-307

ISSN号：0004-9727

关键字：weighted Dirichlet space; composition operator; generalised Nevanlinna counting function; essential norm; angular derivative

摘要：Let phi be an analytic self-map of the unit disc. If phi is analytic in a neighbourhood of the closed unit disc, we give a precise formula for the essential norm of the composition operator C-phi on the weighted Dirichlet spaces D-alpha for alpha > 0. We also show that, for a univalent analytic self-map phi of D, if phi has an angular derivative at some point of partial derivative D, then the essential norm of C-phi on the Dirichlet space is equal to one.