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\(L^{\varphi}(\mu)\)-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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