This paper explores the limiting weak-type behaviors of certain classical operators in harmonic analysis including maximal operators, singular and fractional integral operators and maximal truncated singular integrals as well as the general convolution operators with weak-type Young’s inequalities. Some optimal limiting weak-type behaviors are given, which essentially improve and extend the previous results. As applications, several characterizations on the weak-type endpoint boundedness for fractional integral operators and maximal operators with homogeneous kernels, and the weak-type Young’s inequality for the general convolution operator are also obtained.

中文翻译：

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调和分析中某些经典算子的极限弱型行为

本文探讨了谐波分析中某些经典算子的极限弱型行为，包括最大算子，奇异和分数积分算子和最大截断奇异积分以及具有弱型杨氏不等式的一般卷积算子。给出了一些最佳的限制弱类型行为，这些行为实质上改善和扩展了先前的结果。作为应用，还获得了分数阶算子和具有齐次核的极大算子的弱型端点有界性的一些特征，以及一般卷积算子的弱型杨氏不等式。