Further study on domains and quasihyperbolic distances

Abstract We establish constructive geometric tools for determining when a domain is Ls- averaging and obtain upper and lower bounds for the Ls- integrals of the quasihyperbolic distance. We also construct examples which are helpful to understand our geometric tools and the relationship between p-Poincare domains and Ls- averaging domains. Finally, finite unions of Ls(μ)-averaging domains are explored.