New counterexample constructions yield the exact parabolic Fourier decay rate (d−1)α/d for α in [d−1,d).
Pointwise convergence of the fractional Schr\"odinger equation in $\mathbb R^2$
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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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math.CA 1years
2019 1verdicts
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Upper bounds for Fourier decay rates of fractal measures
New counterexample constructions yield the exact parabolic Fourier decay rate (d−1)α/d for α in [d−1,d).