Möbius invariant spaces in the unit ball

Abstract

In this paper we construct, for arbitrary dimension, a generalisation of the Q_pspaces recently introduced by Gürlebeck et al. We show that they provide a link between the classical Dirichlet and Bloch spaces in the unit ball, and show each of the spaces is invariant for conformal transformations

Keywords:

• Bloch space
• dirichlet space
• conformal maps
• Q_pspaces
• monogenic functions

AMS:

• 30G35
• 30D45