In this note we study the maximal singular integral operators associated with a homogeneous mapping with rough kernels as well as the corresponding maximal operators. The boundedness and continuity on the Lebesgue spaces, Triebel–Lizorkin spaces, and Besov spaces are established for the above operators with rough kernels in $H^{1}({\mathrm{S}}^{n-1})$ , which complement some recent developments related to rough maximal singular integrals.

中文翻译：

---

关于具有粗糙核的最大奇异积分的注记

在本文中，我们研究了与具有粗糙核的齐次映射相关的最大奇异积分算子以及相应的最大算子。为上述带有粗糙核的算子在$ H ^ {1}（{\ mathrm {S}} ^ {n-1}）$中建立Lebesgue空间，Triebel–Lizorkin空间和Besov空间的有界性和连续性。这补充了与粗糙最大奇异积分有关的一些最新发展。