On the exterior product of H\"older differential forms

We introduce a complex of cochains, α-fractional charges (0 < α ≤ 1), whose regularity is between that of De Pauw-Moonens-Pfeffer's charges and that of Whitney's flat cochains. We show that α-H\"older differential forms and their exterior derivative can be realized as α-fractional charges, and that it is possible to define the exterior product between an α-fractional and a β-fractional charge, under the condition that α + β > 1. This construction extends the Young integral in arbitrary dimension and codimension.