Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2018-04-01

Journal: BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY

Included Journals: Scopus、SCIE

Volume: 97

Issue: 2

Page Number: 297-307

ISSN: 0004-9727

Key Words: weighted Dirichlet space; composition operator; generalised Nevanlinna counting function; essential norm; angular derivative

Abstract: 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.