Absolutely continuous functions of several variables and quasiconformal mappings (Q1432738)

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.