Young integration with respect to Hölder charges

In this paper, we present a multidimensional Young integral that enables to integrate Hölder continuous functions with respect to a Hölder charge. It encompasses the integration of Hölder differential forms introduced by Züst: if [Formula: see text] are merely Hölder continuous functions on the cube [Formula: see text] whose Hölder exponents satisfy a certain condition, it is possible to interpret [Formula: see text] as a Hölder charge and thus to make sense of the integral [Formula: see text] over a set [Formula: see text] of finite perimeter.