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

中文翻译：

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变指数Herz空间与变指数Morrey型空间的重合以及这些空间中亚线性算子的有界性

我们介绍了广义的局部和全局Herz空间，它们的所有特征都是可变的。作为主要结果之一，我们证明了变量Morrey类型空间和互补变量Morrey类型空间被包括在这些广义变量Herz空间的尺度中。基于上述包含，我们还证明了广义变量Herz空间中一类亚线性算子的有界性，并将其应用于变量Morrey类型空间及其互补空间。