Journal of Inequalities and Applications 
Volume 6 (2001), Issue 4, Pages 435-449
doi:10.1155/S1025583401000261

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

Abstract

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.