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Decomposition of functions of bounded variation in Ahlfors-regular PI spaces
Abstract
We prove that, on a non-compact Ahlfors-regular PI space, every function of bounded variation f can be decomposed as a countable sum ∑n=1∞ fn of monotone functions of bounded variation fn, in such a way that the total variation of f is the sum of the total variations of the functions fn. Our result extends a Euclidean result of Bianchini and Tonon to the metric setting.
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BibTeX
@misc{bonicatto2026decomposition,
title = {{Decomposition of functions of bounded variation in Ahlfors-regular PI spaces}},
author = {Paolo Bonicatto and Panu Lahti and Enrico Pasqualetto},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.14779},
eprint = {2610.14779},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.14779},
}
RIS
TY - UNPB
TI - Decomposition of functions of bounded variation in Ahlfors-regular PI spaces
AU - Paolo Bonicatto
AU - Panu Lahti
AU - Enrico Pasqualetto
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2610.14779
UR - https://arxiv.org/abs/2610.14779
AB - We prove that, on a non-compact Ahlfors-regular PI space, every function of bounded variation f can be decomposed as a countable sum ∑_n=1^∞ f_n of monotone functions of bounded variation f_n, in such a way that the total variation of f is the sum of the total variations of the functions f_n. Our result extends a Euclidean result of Bianchini and Tonon to the metric setting.
ER -