Author

Sanghyuk Lee

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Preprint Oct 2026

The strong $\ell^r$ spherical maximal function

Let $d\ge3$ and $2\le r<\infty$. We consider the strong maximal operator associated with Euclidean surface averages over the $\ell^r$ unit sphere and independent coordinate dilations. We prove that this operator is bounded on $L^p(\mathbb R^d)$ if and only if \[ p>\max\left\{\frac{d+1}{d-1},\frac{r}{d-1}\right\}. \] We...

Jin-Bong Lee, Sanghyuk Lee, Jeongtae Oh · 0 citations

Preprint Aug 2026

On the endpoint estimate for discrete spherical average over sparse sequences

Let $d\ge5$, and let $A_\lambda$ denote the normalized discrete spherical average on $\mathbb{Z}^d$ with squared radius $\lambda$. For a strictly increasing sequence $(\mu_k)$ of positive integers, set $\lambda_k=\mu_k!$ and consider the lacunary maximal operator $A_\star f:=\sup_k|A_{\lambda_k}f|$. For each fixed $\ga...

Sanghyuk Lee, Ji Li, Chong-Wei Liang et al. · 0 citations