Sharp $L^p$ bounds for the helical maximal function

Andreas Seeger; David Beltran; Jonathan Hickman; Shaoming Guo

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Sharp L^p bounds for the helical maximal function

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arxiv 2102.08272 v1 pith:QHZ4LJ3D submitted 2021-02-16 math.CA

Sharp L^p bounds for the helical maximal function

David Beltran , Shaoming Guo , Jonathan Hickman , Andreas Seeger This is my paper

classification math.CA

keywords functionboundshelicalmaximalsharpalonganalysisaverages

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We establish the $L^p(\mathbb{R}^3)$ boundedness of the helical maximal function for the sharp range $p>3$. Our results improve the previous known bounds for $p>4$. The key ingredient is a new microlocal smoothing estimate for averages along dilates of the helix, which is established via a square function analysis.

Sharp L^p bounds for the helical maximal function

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