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math.CV2014
A generalization of the Clunie--Sheil-Small theorem
Małgorzata Michalska, Andrzej Michalski
In 1984, a simple and useful univalence criterion for harmonic functions was given by Clunie and Sheil-Small, which is usually called the shear construction. However, the applicati…
math.CV2014
Necessary condition for compactness of a difference of composition operators on the Dirichlet space
Małgorzata Michalska, Andrzej Michalski
Let be a self-map of the unit disk and let denote the composition operator acting on the standard Dirichlet space . A necessary condition for compactness of…