PreprintarXiv licencearXiv
Multilinear rough singular integral operators may not be of the weak type at the endpoint
Abstract
We show that m-linear homogeneous rough singular integral operators LLΩ associated with L∞ functions Ω on 𝕊mn−1 with mean value zero may not be bounded from L1(ℝn)×⋯× L1(ℝn) to L1/m,nf(ℝn) except possibly for the case n=1 and m=2.
Related
- Weak Endpoint Estimate for Commutators of Rough Maximal Singular Integral operators
- Weak type (1,1) boundedness of noncommutative singular integral operators with rough kernels
- Weak type (1,1) bound criterion for maximal truncated singular integral operators with rough kernels
- Endpoint estimates for commutators of singular integral operators associated with admissible functions
- Weighted Endpoint Variational and Jump Inequalites for Rough Singular Integrals
BibTeX
@misc{honzik2026multilinear,
title = {{Multilinear rough singular integral operators may not be of the weak type at the endpoint}},
author = {Petr Honzik},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10856},
eprint = {2610.10856},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10856},
}
RIS
TY - UNPB
TI - Multilinear rough singular integral operators may not be of the weak type at the endpoint
AU - Petr Honzik
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.10856
UR - https://arxiv.org/abs/2610.10856
AB - We show that m-linear homogeneous rough singular integral operators LL_Ω associated with L^∞ functions Ω on 𝕊^mn−1 with mean value zero may not be bounded from L^1(ℝ^n)×⋯× L^1(ℝ^n) to L^1/m,nf(ℝ^n) except possibly for the case n=1 and m=2.
ER -