We introduce local and global generalized Herz spaces. As one of the main results we show that Morrey type spaces and complementary Morrey type spaces are included into the scale of these Herz spaces. We also prove the boundedness of a class of sublinear operators in generalized Herz spaces with application to Morrey type spaces and their complementary spaces, based on the mentioned inclusion.

中文翻译：

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Herz空间满足Morrey类型空间和互补Morrey类型空间

我们介绍了局部和全局广义Herz空间。作为主要结果之一，我们表明在这些Herz空间的尺度中包括Morrey型空间和互补型Morrey型空间。基于上述包含，我们还证明了广义Herz空间中一类亚线性算子的有界性，并应用于Morrey型空间及其互补空间。