Young Integration with respect to Hölder Charges
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | |
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| _version_ | 1866912304324411392 |
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| author | Bouafia, Philippe |
| author_facet | Bouafia, Philippe |
| contents | 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 R. Züst: if $f$, $g_1, \dots, g_d$ are merely Hölder continuous functions on the cube $[0, 1]^d$ whose Hölder exponents satisfy a certain condition, it is possible to interpret $\mathrm{d}g_1 \wedge \cdots \wedge \mathrm{d}g_d$ as a Hölder charge and thus to make sense of the integral \[ \int_B f \mathrm{d} g_1 \wedge \cdots \wedge \mathrm{d}g_d \] over a set $B \subset [0, 1]^d$ of finite perimeter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_15423 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Young Integration with respect to Hölder Charges Bouafia, Philippe Functional Analysis Probability 28A25 28C99 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 R. Züst: if $f$, $g_1, \dots, g_d$ are merely Hölder continuous functions on the cube $[0, 1]^d$ whose Hölder exponents satisfy a certain condition, it is possible to interpret $\mathrm{d}g_1 \wedge \cdots \wedge \mathrm{d}g_d$ as a Hölder charge and thus to make sense of the integral \[ \int_B f \mathrm{d} g_1 \wedge \cdots \wedge \mathrm{d}g_d \] over a set $B \subset [0, 1]^d$ of finite perimeter. |
| title | Young Integration with respect to Hölder Charges |
| topic | Functional Analysis Probability 28A25 28C99 |
| url | https://arxiv.org/abs/2401.15423 |