TY - JOUR
T1 - Ahlfors-Weill extensions in several complex variables
AU - Chuaqui, Martin
AU - Hernández, Rodrigo
N1 - Publisher Copyright:
© De Gruyter 2015.
PY - 2015/1/1
Y1 - 2015/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84920973426&partnerID=8YFLogxK
U2 - 10.1515/crelle-2012-0098
DO - 10.1515/crelle-2012-0098
M3 - Article
AN - SCOPUS:84920973426
SN - 0075-4102
SP - 161
EP - 179
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 698
ER -