On the exterior product of Hölder differential forms

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