We obtain a representation for the norm of a composition operator on the Dirichlet space induced by a map of the form φ(z)=az+b. We compare this result to an upper bound for ‖Cφ‖ that is valid whenever φ is univalent. Our work relies heavily on an adjoint formula recently discovered by Gallardo-Gutiérrez and Montes-Rodríguez.
Hammond, Christopher, 2005: The norm of a composition operator with linear symbol acting on the Dirichlet space. Journal of Mathematical Analysis and Applications, 341, no. 2, 636-639.
The views expressed in this paper are solely those of the author.
Initially published in Journal of Mathematical Analysis and Applications, 303 (2005), no. 2, 499–508.
© 2004 Elsevier Inc.