We prove resolvent estimates in the Euclidean setting for Schrodinger operators with potentials in Lebesgue spaces: $-\Delta+V$. The $(L^{2}, L^{p})$ estimates were already obtained by Blair-Sogge-Sire, but we extend their result to other $(L^{p}, L^{q})$ estimates using their idea and the result and method of Kwon-Lee on non-uniform resolvent estimates in the Euclidean space.

中文翻译：

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具有 Lebesgue 空间势的 Schrödinger 算子的解析估计

我们证明了在 Lebesgue 空间中具有势的薛定谔算子的欧几里得设置中的解算估计：$-\Delta+V$。$(L^{2}, L^{p})$ 估计值已经由 Blair-Sogge-Sire 获得，但我们将他们的结果扩展到其他 $(L^{p}, L^{q})$ 估计值使用他们的想法和 Kwon-Lee 的结果和方法对欧几里德空间中的非均匀解析度估计。