Absolutely Continuous Functions of Several Variables and Quasiconformal Mappings

Abstract

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.