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Distortion of Quasiregular Mappings and Equivalent Norms on Lipschitz-Type Spaces

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  • Miodrag Mateljević

Abstract

We prove a quasiconformal analogue of Koebe’s theorem related to the average Jacobian and use a normal family argument here to prove a quasiregular analogue of this result in certain domains in -dimensional space. As an application, we establish that Lipschitz-type properties are inherited by a quasiregular function from its modulo. We also prove some results of Hardy-Littlewood type for Lipschitz-type spaces in several dimensions, give the characterization of Lipschitz-type spaces for quasiregular mappings by the average Jacobian, and give a short review of the subject.

Suggested Citation

  • Miodrag Mateljević, 2014. "Distortion of Quasiregular Mappings and Equivalent Norms on Lipschitz-Type Spaces," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-20, October.
    • Handle: RePEc:hin:jnlaaa:895074
    DOI: 10.1155/2014/895074
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