Compact composition operators on weighted Hilbert spaces of analytic functions

Karim Kellay (1, 2) , Pascal Lefèvre (3)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 IMB - Institut de Mathématiques de Bordeaux
3 LML - Laboratoire de Mathématiques de Lens

We characterize the compactness of composition operators acting on a large family of Hilbert spaces of analytic functions which lie between Bergman and Dirichlet spaces. Our characterization is given in terms of generalized Nevanlinna counting functions.

Mots clés: Weighted analytic spaces; compact composition operators; generalized Nevanlinna counting function.; generalized Nevanlinna counting function

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

Karim Kellay, Pascal Lefèvre. Compact composition operators on weighted Hilbert spaces of analytic functions. Journal of Mathematical Analysis and Applications, 2012, 386 (2), pp.718-727. ⟨hal-00474028⟩