Abstract
We establish constructive geometric tools for determining when a domain is L^{s}-averaging and obtain upper and lower bounds for the L^{s}-integrals of the quasihyperbolic distance. We also construct examples that are helpful to understand our geometric tools and the relationship between p-Poincaré domains and L^{s}-averaging domains. Finally, finite unions of L^{s}(mu )-averaging domains are explored.
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