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The best Musielak-Orlicz approximation by linear subspaces
Abstract
We study best modular approximation in Musielak-Orlicz spaces. A geometric classification near the origin of Orlicz functions is introduced to isolate weighted L1-like behavior. We establish existence results under minimal hypotheses and provide a variational characterization of minimizers via lateral derivatives. Finally, we establish uniqueness criteria, including a one-dimensional Haar-type theorem and characterizations in $0$- and $1$-spaces in higher dimensions.
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BibTeX
@misc{ponce2026best,
title = {{The best Musielak-Orlicz approximation by linear subspaces}},
author = {Juan Costa Ponce and Sergio Favier and Fabián Levis},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20466},
eprint = {2609.20466},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20466},
}
RIS
TY - UNPB
TI - The best Musielak-Orlicz approximation by linear subspaces
AU - Juan Costa Ponce
AU - Sergio Favier
AU - Fabián Levis
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20466
UR - https://arxiv.org/abs/2609.20466
AB - We study best modular approximation in Musielak-Orlicz spaces. A geometric classification near the origin of Orlicz functions is introduced to isolate weighted L^1-like behavior. We establish existence results under minimal hypotheses and provide a variational characterization of minimizers via lateral derivatives. Finally, we establish uniqueness criteria, including a one-dimensional Haar-type theorem and characterizations in $0$- and $1$-spaces in higher dimensions.
ER -