A Self-contained proof of the strong-type capacitary inequality for the Dirichlet space

Omar El-Fallah (1) , Karim Kellay (2) , Javad Mashreghi (3) , Thomas Ransford (3)

1 Département de Mathématiques
2 IMB - Institut de Mathématiques de Bordeaux
3 Département de Mathématiques et de Statistiques

In this expository article, we give a self-contained proof of the strong-type capacitary inequality for functions in the Dirichlet space. We also show that such functions possess boundary limits in exponentially tangential approach regions at almost every point on the unit circle.

Mots clés: Dirichlet space; Capacity; Strong-type inequality; Tangential approach region.; Tangential approach region

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

Omar El-Fallah, Karim Kellay, Javad Mashreghi, Thomas Ransford. A Self-contained proof of the strong-type capacitary inequality for the Dirichlet space. CRM Proceeding and Lecture Notes, Amer Math Soc, Providence, RI, 2011, 55, pp.1-20. ⟨hal-00638564⟩