Journal of Inequalities and Applications
Volume 6 (2001), Issue 4, Pages 435-449

Whitney covers and quasi-isometry of Ls(μ)-averaging domains

Shusen Ding1 and Bing Liu2

1Department of Mathematics, Seattle University, 98122, WA, USA
2Department of Mathematics, Saginaw Valley State University, 7400 Bay Road, University Center, MI 48710, USA

Received 4 November 1999; Revised 9 February 2000

Copyright © 2001 Shusen Ding and Bing Liu. 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.


This is a part of our series studies about the Ls(μ)-averaging domains. In this paper, we first characterize Ls(μ)-averaging domains using the Whitney covers. Then we prove the invariance of Ls(μ)-averaging domains under some mappings, such as K-quasi-isometric mappings, φ-quasi-isometric mappings.