We prove uniform Sobolev estimates for the resolvent of Schr\"odinger operators with large scaling-critical potentials without any repulsive condition. As applications, global-in-time Strichartz estimates including some non-admissible retarded estimates, a H\"ormander type spectral multiplier theorem, and Keller type eigenvalue bounds with complex-valued potentials are also obtained.

中文翻译：

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具有标度临界潜力和应用的薛定谔算子的统一 Sobolev 估计

我们证明了 Schr\"odinger 算子的解算符的统一 Sobolev 估计，没有任何排斥条件。作为应用，全局时间 Strichartz 估计包括一些不可允许的延迟估计，H\"Ormander 型谱乘子定理，并获得了具有复值势的 Keller 型特征值界。