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.
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Stanislav Hencl, Absolutely Continuous Functions of Several Variables and Quasiconformal Mappings. Z. Anal. Anwend. 22 (2003), no. 4, pp. 767–778DOI 10.4171/ZAA/1172