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arXiv · 2109.00382

A global space-time estimate for dispersive operators through its local estimate

Chu-hee Cho·Youngwoo Koh·Jungjin Lee
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Abstract

We will show that a local space-time estimate implies a global space-time estimate for dispersive operators. In order for this implication we consider a Littlewood-Paley type square function estimate for dispersive operators in a time variable and a generalization of Tao's epsilon removal lemma in mixed norms. By applying this implication to the fractional Schrodinger equation in R^{2+1} we obtain the sharp global space-time estimates with optimal regularity from the previous known local ones.

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Chu-hee Cho, Youngwoo Koh, Jungjin Lee. 2021-09-01. A global space-time estimate for dispersive operators through its local estimate. https://arxiv.org/abs/2109.00382

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