Weak type (1,1) bound criterion for maximal truncated singular integral operators with rough kernels
Year: 2026
Type: preprint
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 $Ω\in L\log L(\sS^{d-1})$ 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.
Source: arXiv (Cornell University)
Authors: Lai, Xudong, Xu, Lingxin
Institution: Harbin Institute of Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7221753413