Copyright © 2010 Yuming Xing. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove both local and global Poincaré inequalities with
Luxemburg norms for differential forms in -averaging domains, which can be considered as generalizations of the existing versions of Poincaré inequalities.