PreprintarXiv licencearXiv
A Direct Approach to Rough Paths in Time-Weighted Besov Spaces
Abstract
We extend the Besov rough path framework of Friz and Seeger to paths lying in Besov spaces that are Muckenhoupt-weighted in time. We establish a weighted Besov sewing lemma, construct Young and rough integrals, and prove local Lipschitz continuity of the Itô-Lyons map in weighted Besov norms. The resulting estimates deliver "location-sensitive" control of errors in RDE solution increments. We illustrate the framework with a diffusion whose coefficient is singular at a specified time.
Related
- Small Hankel operators on weighted Besov spaces
- Jackson and Bernstein Inequalities with Explicit Weight Dependence for Band-Limited Wavelet Approximation in Weighted Besov Spaces
- Preduals of weighted homogeneous Bourgain-Morrey Besov-Triebel-Lizorkin spaces associated with operators
- Minimum-Norm Interpolation in Weighted Variation Spaces: Direct and Inverse Problems
- Approximate Transitivity of Young Translation on Rough Paths
BibTeX
@misc{gupta2026direct,
title = {{A Direct Approach to Rough Paths in Time-Weighted Besov Spaces}},
author = {Atiksh Gupta},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28548},
eprint = {2609.28548},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28548},
}
RIS
TY - UNPB
TI - A Direct Approach to Rough Paths in Time-Weighted Besov Spaces
AU - Atiksh Gupta
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28548
UR - https://arxiv.org/abs/2609.28548
AB - We extend the Besov rough path framework of Friz and Seeger to paths lying in Besov spaces that are Muckenhoupt-weighted in time. We establish a weighted Besov sewing lemma, construct Young and rough integrals, and prove local Lipschitz continuity of the Itô-Lyons map in weighted Besov norms. The resulting estimates deliver "location-sensitive" control of errors in RDE solution increments. We illustrate the framework with a diffusion whose coefficient is singular at a specified time.
ER -