A note on local smoothing estimates for fractional Schrödinger equations

Gan, Shengwen; Oh, Changkeun; Wu, Shuizhu

doi:10.48550/arxiv.2109.05401

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Local Smoothing Estimates For the Fractional Schrödinger Equ...1

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2022

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“…It should be noted that Gan-Oh-Wu [8] considered the local smoothing problem for the fractional Schrödinger equation via a different approach and mentioned essentially the same method as above discussed. Furthermore, it is possible to further improve Gan-Oh-Wu's result by considering the Hörmanger type operator with the convex and straight conditions using Wang's method [28] at least in dimension n = 2.…”

Section: Local Smoothing Estimates For the Fractional Schrödinger Equ...mentioning

confidence: 99%

A type of oscillatory integral operator and its applications

Gao

Wang

2022

Math. Z.

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In this paper, we consider $$L^p$$ L p - estimate for a class of oscillatory integral operators satisfying the Carleson–Sjölin conditions with further convex and straight assumptions. As applications, the multiplier problem related to a general class of hypersurfaces with nonvanishing Gaussian curvature, local smoothing estimates for the fractional Schrödinger equation and the sharp resolvent estimates outside of the uniform boundedness range are discussed.

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Section: Local Smoothing Estimates For the Fractional Schrödinger Equ...mentioning

confidence: 99%