Cyclic vectors in Korenblum type spaces

Abdelouahab Hanine (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

In this paper we use the technique of premeasures, introduced by Korenblum in the 1970-s, to give a characterization of cyclic functions in the Korenblum type spaces $\mathcal{A}_{\Lambda}^{-\infty }$. In particular, we give a positive answer to a conjecture by Deninger \cite[Conjecture 42]{CD}.

Mots clés: Korenblum type space; premeasure; $\Lambda$-Carleson set; cyclic function; $\Lambda$-singular part of premeasure

Domaines: Analyse fonctionnelle [math.FA]

Abdelouahab Hanine. Cyclic vectors in Korenblum type spaces. 2012. ⟨hal-00807339v2⟩