Ahlfors-Weill extensions in several complex variables

Martin Chuaqui, Rodrigo Hernández

Research output: Contribution to journalArticlepeer-review

Abstract

We derive an Ahlfors-Weill type extension for a class of holomorphic mappings defined in the ball script Bn, generalizing the formula for Nehari mappings in the disk. The class of mappings holomorphic in the ball is defined in terms of the Schwarzian operator. Convexity relative to the Bergman metric plays an essential role, as well as the concept of a weakly linearly convex domain. The extension outside the ball takes values in the projective dual to script Cn, that is, in the set of complex hyperplanes.

Original languageEnglish
Pages (from-to)161-179
Number of pages19
JournalJournal fur die Reine und Angewandte Mathematik
Issue number698
DOIs
StatePublished - 1 Jan 2015

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