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A Helmholtz-Weyl decomposition for Hölder spaces. A nonvariational approach
Abstract
We prove a form of the fundamental theorem of vector calculus for Hölder continuous vector fields with no assumption on the derivatives that exploits Schauder spaces with negative exponents. Then by developing an idea of von Wahl in the context of Lebesgue spaces, we prove a form of the Helmholtz Weyl decomposition Theorem for spaces of Hölder continuous functions, with explicit formulas for the projection operators.
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BibTeX
@misc{cristoforis2026helmholtzweyl,
title = {{A Helmholtz-Weyl decomposition for Hölder spaces. A nonvariational approach}},
author = {M. Lanza de Cristoforis},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.18241},
eprint = {2609.18241},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18241},
}
RIS
TY - UNPB
TI - A Helmholtz-Weyl decomposition for Hölder spaces. A nonvariational approach
AU - M. Lanza de Cristoforis
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.18241
UR - https://arxiv.org/abs/2609.18241
AB - We prove a form of the fundamental theorem of vector calculus for Hölder continuous vector fields with no assumption on the derivatives that exploits Schauder spaces with negative exponents. Then by developing an idea of von Wahl in the context of Lebesgue spaces, we prove a form of the Helmholtz Weyl decomposition Theorem for spaces of Hölder continuous functions, with explicit formulas for the projection operators.
ER -