Composition operators on the polydisk induced by affine maps

Frédéric Bayart (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

We study the continuity of composition operators on the classical Hardy and weighted Bergman spaces of the polydisk. We show that this problem involves some delicate properties of the derivative of the symbol. In particular, we characterize continuity when the symbol is a linear self-map of the polydisk

Domaines: Analyse fonctionnelle [math.FA]

Frédéric Bayart. Composition operators on the polydisk induced by affine maps. Journal of Functional Analysis, 2011, 260 (7), pp.1969-2003. ⟨10.1016/j.jfa.2010.12.019⟩. ⟨hal-00648720⟩