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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

Chuanwei Gao , Bochen Liu , Changxing Miao , Yakun Xi This is my paper · ORCID
classification math.APmath.CA
keywords classdimensionsestimateestimatesfunctionsimprovedlocalphase
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abstract

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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  1. H\"ormander oscillatory integral operators: a revisit

    math.AP 2025-05 conditional novelty 6.0 of 10

    The paper contributes new, scale-dependent induction proofs of the known sharp Lp estimate and decoupling theorem for Hörmander oscillatory integral operators.

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