$L^p$ bound on the strong spherical maximal function

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arxiv 2309.15308 v1 pith:SXKVMOZK submitted 2023-09-26 math.CA

Juyoung Lee , Sanghyuk Lee , Sewook Oh This is my paper · ORCID

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keywords functionmaximalsphericalstrongboundboundedmathbbnote

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abstract

In this note we show that the strong spherical maximal function in $\mathbb R^d$ is bounded on $L^p$ if $p>2(d+1)/(d-1)$ for $d\ge 3$.

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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.