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Improved local smoothing estimate for the wave equation in higher dimensions

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arxiv 2108.06870 v2 pith:C2CSTJTU submitted 2021-08-16 math.AP math.CA

Improved local smoothing estimate for the wave equation in higher dimensions

Chuanwei Gao , Bochen Liu , Changxing Miao , Yakun Xi This is my paper
classification math.AP math.CA
keywords classdimensionsestimateestimatesfunctionsimprovedlocalphase
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In this paper, we establish the sharp $k$-broad estimate for a class of phase functions satisfying the homogeneous convex conditions. As an application, we obtain improved local smoothing estimates for the half-wave operator in dimensions $n\ge3$. As a byproduct, we also generalize the restriction estimates of Ou--Wang to a broader class of phase functions.

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