In this paper, we provide the boundedness property of the Riesz transforms associated to the Schrodinger operator $\mathcal{L}=-\Delta + \mathbf{V}$ in a new weighted Morrey space which is the generalized version of many previous Morrey type spaces. The additional potential $\V$ considered in this paper is a non-negative function satisfying the suitable reverse Holder's inequality. Our results are new and general in many cases of problems. As an application of the boundedness property of these singular integral operators, we obtain some regularity results of solutions to Schrodinger equations in the new Morrey space.

中文翻译：

---

广义莫雷空间中与薛定谔算符相关的奇异积分算符的有界性及其应用

在本文中，我们提供了与薛定谔算子 $\mathcal{L}=-\Delta + \mathbf{V}$ 相关的 Riesz 变换的有界性质，该空间是许多以前的 Morrey 空间的广义版本。键入空格。本文考虑的附加势$\V$是一个满足合适的反向Holder不等式的非负函数。在许多问题的情况下，我们的结果是新的和普遍的。作为这些奇异积分算子的有界性的应用，我们得到了新莫雷空间中薛定谔方程解的一些正则性结果。