$$L^{\varphi}(\mu)$$-averaging domains and the quasi-hyperbolic metric.(English)Zbl 1063.30022

Summary: We first introduce $$L^{\varphi}(\mu)$$-averaging domains which are generalizations of existing domains, such as John domains and $$L^{s}(\mu)$$-averaging domains. Then, we characterize $$L^{\varphi}(\mu)$$-averaging domains using the quasihyperbolic metric. Finally, we give applications to quasiconformal mappings.

MSC:

 30C65 Quasiconformal mappings in $$\mathbb{R}^n$$, other generalizations
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References:

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