We consider subspaces of Morrey spaces defined in terms of various vanishing properties of functions. Such subspaces were recently used to describe the closure of $C_0^\infty(\mathbb{R}^n)$ in Morrey norm. We show that these subspaces are invariant with respect to some classical operators of harmonic analysis, such as the Hardy-Littlewood maximal operator, singular type operators and Hardy operators. We also show that the vanishing properties defining those subspaces are preserved under the action of Riesz potential operators and fractional maximal operators.

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关于某些经典算子的 Morrey 空间的某些消失子空间的不变性

我们考虑根据函数的各种消失性质定义的 Morrey 空间的子空间。这些子空间最近被用来描述莫雷范数中 $C_0^\infty(\mathbb{R}^n)$ 的闭包。我们证明这些子空间对于一些经典的调和分析算子是不变的，例如 Hardy-Littlewood 极大值算子、奇异型算子和 Hardy 算子。我们还表明，在 Riesz 潜在算子和分数极大值算子的作用下，定义这些子空间的消失特性得以保留。