L^φ(μ)-averaging domains and the quasi-hyperbolic metric

Abstract

In this paper, we first introduce Lℓ(μ)-averaging domains which are generalizations of existing domains, such as John domains and L^s(μ)-averaging domains. Then, we characterize L^φ(μ)-averaging domains using the quasihyperbolic metric. Finally, we give applications to quasiconformal mappings.