In this paper, we first give some new characterizations of Muckenhoupt type weights through establishing the boundedness of maximal operators on the weighted Lorentz and Morrey spaces. Secondly, we establish the boundedness of sublinear operators including many interesting in harmonic analysis and its commutators on the weighted Morrey spaces. Finally, as an application, the boundedness of strongly singular integral operators and commutators with symbols in BMO space are also given.

中文翻译：

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加权Lorentz和Morrey空间上的最大算子和奇异积分

在本文中，我们首先通过在加权Lorentz和Morrey空间上建立最大算子的有界性来给出Muckenhoupt型权重的一些新特征。其次，我们建立了亚线性算子的有界性，其中包括谐波分析中的许多有趣问题及其在加权Morrey空间上的交换子。最后，作为一个应用，还给出了BMO空间中具有符号的强奇异积分算子和交换子的有界性。