Cyclicity of singular inner functions from the corona theorem

Omar El-Fallah (1) , Karim Kellay (2, 3) , Kristian Seip (4)

1 Département de Mathématiques
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités
3 IMB - Institut de Mathématiques de Bordeaux
4 Department of Mathematical Sciences

Carleson's corona theorem is used to obtain two results on cyclicity of singular inner functions in weighted Bergman-type spaces on the unit disk. Our method proof requires no regularity conditions on the weights.

Mots clés: Weighted Bergman space; cyclic function; singular inner function; corona theorem

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

Omar El-Fallah, Karim Kellay, Kristian Seip. Cyclicity of singular inner functions from the corona theorem. Journal of the Institute of Mathematics of Jussieu, 2011, 11 (4), pp.815-824. ⟨10.1017/S1474748012000035⟩. ⟨hal-00550574⟩