In this paper, assume that is a Schrödinger operator on the Heisenberg group , where the nonnegative potential belongs to the reverse Hölder class . By the aid of the subordinate formula, we investigate the regularity properties of the time-fractional derivatives of semigroups and , respectively. As applications, using fractional square functions, we characterize the Hardy-Sobolev type space associated with . Moreover, the fractional square function characterizations indicate an equivalence relation of two classes of Hardy-Sobolev spaces related with .

中文翻译：

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与薛定inger算子有关的半群的时间分数阶导数的正则性及其在海森堡群上的Hardy-Sobolev空间中的应用

在本文中，假设 是Heisenberg集团的Schrödinger算子，非负势属于反向Hölder类。由从属式的辅助下，我们研究半群的时间分数阶导数的正则性和，分别。作为应用程序，我们使用分数平方函数来表征与关联的Hardy-Sobolev类型空间。此外，分数平方函数特征表示与相关的两类Hardy-Sobolev空间的等价关系。