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Pointwise convergence of the fractional Schr\"odinger equation in $\mathbb R^2$

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arxiv 1809.03246 v3 pith:DIJNOIXE submitted 2018-09-10 math.AP

Chu-hee Cho , Hyerim Ko This is my paper · ORCID
classification math.AP
keywords mathbbestimatesconvergenceequationfractionalobtainedodingerpointwise
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abstract

We investigate the pointwise convergence of the solution to the fractional Schr\"odinger equation in $\mathbb R^2$. By establishing $H^s(\mathbb R^2)-L^3(\mathbb R^2)$ estimates for the associated maximal operator provided that $s>1/3$, we improve the previous result obtained by Miao, Yang, and Zheng. Our estimates extend the refined Strichartz estimates obtained by Du, Guth, and Li to a general class of elliptic functions.

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  1. Upper bounds for Fourier decay rates of fractal measures

    math.CA 2019-08 accept novelty 7.0 of 10

    New counterexample constructions yield the exact parabolic Fourier decay rate (d−1)α/d for α in [d−1,d).

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