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

Ding, Shusen

Comput. Math. Appl. 47, No. 10-11, 1611-1618 (2004).

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

Keywords:

Domains; Mappings; Measures; Weights; Quasihyperbolic metric

References:

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