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Weak type (1,1) bound criterion for maximal truncated singular integral operators with rough kernels
Abstract
This paper proves the weak type (1,1) boundedness for maximal truncated singular integral operators with rough non-convolution kernels of the form $Ω(x-y) K(x,y)$, where Ω is homogeneous of degree zero with Ω∈ Llog L(sSd−1) and K is a standard Calderón-Zygmund kernel. This extends the recent resolution of the classical convolution case by Lai \cite{Lai2025weak} to a wider class of operators.
Related
- Weak Endpoint Estimate for Commutators of Rough Maximal Singular Integral operators
- Weak type (1,1) estimates for noncommutative maximal truncated rough singular integrals
- Two pointwise estimates for singular integral operators over p-adic groups
- Weak type (1,1) boundedness of noncommutative singular integral operators with rough kernels
- Essentially semi-commuting singular integral operators with Cauchy kernel on L2
BibTeX
@misc{lai2026weak,
title = {{Weak type (1,1) bound criterion for maximal truncated singular integral operators with rough kernels}},
author = {Xudong Lai and Lingxin Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15820},
eprint = {2610.15820},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15820},
}
RIS
TY - UNPB
TI - Weak type (1,1) bound criterion for maximal truncated singular integral operators with rough kernels
AU - Xudong Lai
AU - Lingxin Xu
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15820
UR - https://arxiv.org/abs/2610.15820
AB - This paper proves the weak type (1,1) boundedness for maximal truncated singular integral operators with rough non-convolution kernels of the form $Ω(x-y) K(x,y)$, where Ω is homogeneous of degree zero with Ω∈ Llog L(sS^d−1) and K is a standard Calderón-Zygmund kernel. This extends the recent resolution of the classical convolution case by Lai \cite{Lai2025weak} to a wider class of operators.
ER -