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A multi-parameter cinematic curvature

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arxiv 2306.01606 v7 pith:UDWCZAFB submitted 2023-06-02 math.CA

Mingfeng Chen , Shaoming Guo , Tongou Yang This is my paper · ORCID
classification math.CA
keywords cinematiccurvaturemulti-parameterboundsconditionconjecturelocalmaximal
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abstract

We state a multi-parameter cinematic curvature condition, and prove $L^p$ bounds for related maximal operators. In particular, we verify a local smoothing conjecture of Zahl.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Improved $L^p$ bounds for the strong spherical maximal operator

    math.CA 2025-02 accept novelty 8.0 of 10

    For all n≥3 and p>2, the strong spherical maximal operator is bounded on Lp, resolving the sharp n=3 case of the strong spherical maximal conjecture.

  2. Lacunary $\delta$-Discretised Spherical Maximal Operators

    math.CA 2025-07 conditional novelty 6.0 of 10

    Lacunary delta-discretised spherical maximal operators are Lp bounded for 1<p<infinity and H1 to weak L1, with constants independent of delta; the multi-parameter variant is also Lp bounded.

  3. Improved packing of hypersurfaces in $\mathbb R^d$

    math.CA 2025-01 accept novelty 6.0 of 10

    The authors pack every d-sphere of radii 1 to 2 into a set whose δ-neighborhood has measure ≲ |log δ|^{-2/d}, matching the lower bound in two dimensions.

  4. Spherical maximal estimates via geometry

    math.CA 2024-12 conditional novelty 6.0 of 10

    A Fourier-free geometric argument bounds a discretized spherical maximal operator on L^p with logarithmic loss.

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