The Lindelöf principle in several complex variables

We formulate and prove a new Lindelöf principle in the function theory of several complex variables. Inspired by the classical result, as improved later by Lehto and Virtanen, this new result meshes closely with the well-established Fatou theorems of Koranyi and Stein. In particular, this is a Lindelöf principle for admissible approach regions. We further adapt the new principle to the Levi geometry of various domains. The results in this paper improve on earlier results of Cirka, Cima/Krantz, Abate, and Abate/Tauraso.