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A note on the Besov spaces B1Φ2
Abstract
Regarding the Besov space B1Φ2, defined by S. Geiss and Ylinen (Memoirs AMS 1335, 2021) by a coupling method, we prove for ξ∈B1Φ2 ∩ L2 a distributional estimate in terms of the Lorentz-Zygmund space L1,∞(ln L)−1 for the Malliavin derivative D(Tuξ) uniformly in u>0, where (Tu)u≥ is the Ornstein-Uhlenbeck semi-group. Here ξ is not necessarily Malliavin differentiable in the D1,1-sense. This provides for Theorem 4.22 of the aforementioned reference an extension to the borderline case p=1.
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BibTeX
@misc{geiss2026note,
title = {{A note on the Besov spaces $\rm B_1^Φ_2$}},
author = {Stefan Geiss},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.36152},
eprint = {2610.36152},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.36152},
}
RIS
TY - UNPB
TI - A note on the Besov spaces B_1^Φ_2
AU - Stefan Geiss
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.36152
UR - https://arxiv.org/abs/2610.36152
AB - Regarding the Besov space B_1^Φ_2, defined by S. Geiss and Ylinen (Memoirs AMS 1335, 2021) by a coupling method, we prove for ξ∈B_1^Φ_2 ∩ L_2 a distributional estimate in terms of the Lorentz-Zygmund space L_1,∞(ln L)^−1 for the Malliavin derivative D(T_uξ) uniformly in u>0, where (T_u)_u≥ is the Ornstein-Uhlenbeck semi-group. Here ξ is not necessarily Malliavin differentiable in the D_1,1-sense. This provides for Theorem 4.22 of the aforementioned reference an extension to the borderline case p=1.
ER -