We define a scale of weighted Morrey spaces which contains different weighted versions appearing in the literature. This allows us to obtain weighted estimates for operators in a unified way. In general, we obtain results for weights of the form $|x|^\alpha w(x)$ with $w\in A_p$ and nonnegative $\alpha$. We study particularly some properties of power-weighted spaces and in the case of the Hardy-Littlewood maximal operator our results for such spaces are sharp. By using extrapolation techniques the results are given in abstract form in such a way that they are automatically obtained for many operators.

中文翻译：

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加权莫雷空间族中的有界属性，强调幂权重

我们定义了一个加权莫雷空间的尺度，其中包含出现在文献中的不同加权版本。这使我们能够以统一的方式获得运营商的加权估计。一般而言，我们获得 $|x|^\alpha w(x)$ 形式的权重结果，其中 $w\in A_p$ 和非负 $\alpha$。我们特别研究了幂加权空间的一些特性，在 Hardy-Littlewood 极大算子的情况下，我们对这些空间的结果非常清晰。通过使用外推技术，结果以抽象形式给出，许多操作员可以自动获得这些结果。