We prove some weighted refinements of the classical Strichartz inequalities for initial data in the Sobolev spaces Ḣ^s(ℝⁿ). We control the weightedL ²-norm of the solution of the free Schrödinger equation whenever the weight is in a Morrey-Campanato type space adapted to that equation. Our partial positive results are complemented by some necessary conditions based on estimates for certain particular solutions of the free Schrödinger equation.

中文翻译：

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Morrey-Campanato类中权重的Strichartz不等式

我们证明了Sobolev空间^s（some ⁿ）中初始数据的经典Strichartz不等式的一些加权细化。只要权重处于适合该方程的Morrey-Campanato型空间中，我们就控制自由Schrödinger方程解的加权L ²范数。基于对自由Schrödinger方程的某些特定解的估计，我们的部分积极结果得到了一些必要条件的补充。