Geodesic
Some Properties of Composition Operators on the Dirichlet Space
Acta mathematica Universitatis Comenianae, Tome 74 (2005) no. 2 
G. A. Chacon; G. R. Chacon. Some Properties of Composition Operators on the Dirichlet Space. Acta mathematica Universitatis Comenianae, Tome 74 (2005) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2005_74_2_a11/
@article{AMUC_2005_74_2_a11,
     author = {G. A. Chacon and G. R. Chacon},
     title = {Some {Properties} of {Composition} {Operators} on the {Dirichlet} {Space}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2005},
     volume = {74},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2005_74_2_a11/}
}
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Voir la notice de l'article provenant de la source Comenius University

In this paper we investigate composition operators induced on the Dirichlet space by linear fractional maps. We characterize the essential normality in this setting, obtain conditions for the linear fractional symbols j and y of the unit disc for which C j C y * or C y * C j is compact, and investigate the shape of the numerical range for linear fractional composition operators induced on the Dirichlet space.