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Strichartz inequalities with weights in Morrey-Campanato classes
Collectanea Mathematica ( IF 0.7 ) Pub Date : 2010 , DOI: 10.1007/bf03191225
J. A. Barceló , J. M. Bennett , A. Carbery , A. Ruiz , M. C. Vilela

We prove some weighted refinements of the classical Strichartz inequalities for initial data in the Sobolev spaces Ḣs(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:

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。
更新日期:2020-09-21
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