## Abstract and Applied Analysis

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

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 $n$-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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 895074, 20 pages.

Dates
First available in Project Euclid: 27 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1425049702

Digital Object Identifier
doi:10.1155/2014/895074

Mathematical Reviews number (MathSciNet)
MR3273917

Zentralblatt MATH identifier
07023261

#### Citation

Mateljević, Miodrag. Distortion of Quasiregular Mappings and Equivalent Norms on Lipschitz-Type Spaces. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 895074, 20 pages. doi:10.1155/2014/895074. https://projecteuclid.org/euclid.aaa/1425049702

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