Contact points and Schatten composition operators

Hannah Benazouz (1) , Omar El-Fallah (1) , Karim Kellay (2) , Houssame Mahzouli (1)

1 Département de Mathématiques
2 IMB - Institut de Mathématiques de Bordeaux

We study composition operators on Hardy and Dirichlet spaces belonging to Schatten classes. We give some new examples and analyse the size of contact set of the symbol of such operators.

Mots clés: Hardy space; Dirichlet space; composition operators; capacity; level set; Schatten classes

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

Hannah Benazouz, Omar El-Fallah, Karim Kellay, Houssame Mahzouli. Contact points and Schatten composition operators. Mathematische Zeitschrift, 2015, 279 (1-2), pp.407-422. ⟨hal-00950738v2⟩