Distortion of Quasiregular Mappings and Equivalent Norms on Lipschitz-Type Spaces
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 n-dimensional space. As an application, we establish that Lipschitz-type properties are inherited by a qua...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/895074 |
| Summary: | 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 n-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. |
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| ISSN: | 1085-3375 1687-0409 |