Absolutely continuous functions of several variables and quasiconformal mappings (Q1432738)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Absolutely continuous functions of several variables and quasiconformal mappings |
scientific article; zbMATH DE number 2075229
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Absolutely continuous functions of several variables and quasiconformal mappings |
scientific article; zbMATH DE number 2075229 |
Statements
Absolutely continuous functions of several variables and quasiconformal mappings (English)
0 references
15 June 2004
0 references
Summary: We prove that functions with bounded \(n\)-variation and \(n\)-absolutely continuous functions of \(n\)-variables in the sense of [\textit{S. Hencl}, Fundam. Math. 173, No. 2, 175--189 (2002; Zbl 1002.26007)] are stable under quasiconformal mappings. The class of quasiconformal mappings is the best possible since every homeomorphism which induces a bounded operator between \(\text{BV}^n\) spaces is a quasiconformal mapping.
0 references
absolute continuity
0 references
functions of bounded variation
0 references
quasiconformal maps
0 references
