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Zeitschrift für Analysis und ihre Anwendungen


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Volume 22, Issue 4, 2003, pp. 767–778
DOI: 10.4171/ZAA/1172

Published online: 2003-12-31

Absolutely Continuous Functions of Several Variables and Quasiconformal Mappings

Stanislav Hencl[1]

(1) Charles University, Prague, Czech Republic

We prove that functions with bounded n-variation and n-absolutely continuous functions of n-variables in the sense introduced previously by the author [Fund. Math. 173 (2002) 175--189] are stable under quasiconformal mappings. The class of quasiconformal mappings is the best possible since every homeomorphism which induces a bounded operator between BVn spaces is a quasiconformal mapping.

Keywords: Absolute continuity in several variables, quasiconformal maps

Hencl Stanislav: Absolutely Continuous Functions of Several Variables and Quasiconformal Mappings. Z. Anal. Anwend. 22 (2003), 767-778. doi: 10.4171/ZAA/1172