Nevanlinna counting function and Carleson function of analytic maps

Pascal Lefèvre (1) , Daniel Li (1) , Hervé Queffélec (2) , Luis Rodriguez-Piazza (3)

1 LML - Laboratoire de Mathématiques de Lens
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 Departamento de Analisis Matematico

We show that the maximal Nevanlinna counting function and the Carleson function of analytic self-maps of the unit disk are equivalent, up to constants. We give some applications to composition operators on Hardy spaces and on Hardy-Orlicz spaces.

Mots clés: Carleson function; Carleson measure; composition operator; Nevanlinna counting function

Domaines: Analyse fonctionnelle [math.FA]; Variables complexes [math.CV]

Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. Nevanlinna counting function and Carleson function of analytic maps. 2009. ⟨hal-00375955v2⟩