Level sets and Composition operators on the Dirichlet space

O. El-Fallah (1) , K. Kellay (2) , M. Shabankhah (2) , H. Youssfi (2)

1 Département de Mathématiques
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We consider composition operators in the Dirichlet space of the unit disc in the plane. Various criteria on boundedness, compactness and Hilbert-Schmidt class membership are established. Some of these criteria are shown to be optimal.

Mots clés: Dirichlet space; composition operators; capacity

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

O. El-Fallah, K. Kellay, M. Shabankhah, H. Youssfi. Level sets and Composition operators on the Dirichlet space. Journal of Functional Analysis, 2011, 260 ((6)), pp.1721-1733. ⟨hal-00466832⟩