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Improved local smoothing estimates for the fractional Schrödinger operator

Improved local smoothing estimates for the fractional Schrödinger operator 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). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Improved local smoothing estimates for the fractional Schrödinger operator

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References (12)

Publisher
Wiley
Copyright
© 2022 London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms.12556
Publisher site
See Article on Publisher Site

Abstract

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).

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Feb 1, 2022

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