Open AccessExtendability of proper holomorphic mappings and global analytic hypoellipticity of the ∂̄-Neumann problem
Author(s) -
Steven R. Bell
Publication year - 1981
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.78.11.6600
Subject(s) - holomorphic function , bounded function , mathematics , hypoelliptic operator , domain (mathematical analysis) , boundary (topology) , identity theorem , pure mathematics , projection (relational algebra) , neumann boundary condition , mathematical analysis , discrete mathematics , algorithm , differential operator , semi elliptic operator
In this communication, the proof of the following theorem is sketched: IfD 1 is a bounded domain in Cn with real analytic boundary whose ∂̄-Neumann problem is globally real analytic hypoelliptic andf is a proper holomorphic mapping ofD 1 onto a second bounded domainD 2 in Cn with real analytic boundary, then the mappingf extends to be holomorphic in a neighborhood of ¯D1 . The proof relies on a transformation formula for the Bergman projection under proper holomorphic mappings.