Whitney covers and quasi-isometry of <inline-formula><graphic file="1029-242X-2001-647546-i1.gif"/></inline-formula>-averaging domains

• Main Authors: Liu Bing, Ding Shusen
• Format: Article
• Language: English
• Published: SpringerOpen 2001-01-01
• Series: Journal of Inequalities and Applications
• Subjects: L^s(&#956;)-averaging domain; Whitney covers; &#966;-quasi-isometry
• Online Access: http://www.journalofinequalitiesandapplications.com/content/6/647546
• ISSN: 1025-5834; 1029-242X

<p/> <p>This is a part of our series studies about the <inline-formula><graphic file="1029-242X-2001-647546-i2.gif"/></inline-formula>-averaging domains. In this paper, we first characterize <inline-formula><graphic file="1029-242X-2001-647546-i3.gif"/></inline-formula>-averaging domains using the Whitney covers. Then we prove the invariance of <inline-formula><graphic file="1029-242X-2001-647546-i4.gif"/></inline-formula>-averaging domains under some mappings, such as <inline-formula><graphic file="1029-242X-2001-647546-i5.gif"/></inline-formula>-quasi-isometric mappings, <inline-formula><graphic file="1029-242X-2001-647546-i6.gif"/></inline-formula>-quasi-isometric mappings.</p>