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J. Bennett, A. Carbery, T. Tao (2006)
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Harmonic analysis: real‐variable methods, orthogonality, and oscillatory integrals
In this paper, we consider local smoothing estimates for the fractional Schrödinger operator eit(−Δ)α/2$e^{it(-\Delta )^{\alpha /2}}$ with α>1$\alpha >1$. Using the k$k$‐broad ‘norm’ estimates of Guth–Hickman–Iliopoulou (Acta Math. 223 (2019), 251–376), we improve the previously best‐known results of local smoothing estimates of Guo–Roos–Yung (arXiv:1710.10988 (2017)) and Rogers–Seeger (J. Für Die Reine und Ang. Math. (Crelles Journal), 640 (2010), 47–66).
Bulletin of the London Mathematical Society – Wiley
Published: Feb 1, 2022
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