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math.FA2026
Fractional currents and Young geometric integration
Philippe Bouafia
We introduce a class of flat currents with fractal properties, called fractional currents, which satisfy a compactness theorem and remain stable under pushforwards by Hölder conti…
math.FA2026
Non-absolute integration and application to Young geometric integration
Philippe Bouafia
We survey several non-absolutely convergent integrals, including the Henstock-Kurzweil and Pfeffer integrals, and use ideas from these theories to investigate the problem of multid…
math.FA2024
Young Integration with respect to Hölder Charges
Philippe Bouafia
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 diff…