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arXiv · 2110.11185

Circular average relative to fractal measures

Seheon Ham·Hyerim Ko·Sanghyuk Lee
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Abstract

We prove new $L^p$- $L^q$ estimates for averages over dilates of the circle with respect to $\alpha$-dimensional fractal measure, which unify different types of maximal estimates for the circular average. Our results are consequences of $L^p$- $L^q$ smoothing estimates for the wave operator relative to fractal measures. We also discuss similar results concerning the spherical averages.

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Seheon Ham, Hyerim Ko, Sanghyuk Lee. 2021-10-21. Circular average relative to fractal measures. https://doi.org/10.3934/cpaa.2022100

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