References & Citations
Mathematics > Classical Analysis and ODEs
Title: A note on generalized spherical maximal means
(Submitted on 16 Apr 2024 (v1), last revised 18 Apr 2024 (this version, v2))
Abstract: The goal of this note is to provide an alternative proof of Theorem 1.1 (i) in [4], that is, if $n\geq 2$ and $M^{\alpha}$ is bounded on $L^{p}(\mathbb{R}^{n})$ for some $\alpha\in \mathbb{C}$ and $p\geq 2$, then we have
\begin{align*}
\operatorname{Re} \alpha\geq \max\left\{\frac{1-n}{2}+\frac{1}{p},\frac{1-n}{p}\right\}.
\end{align*}
Submission history
From: Feng Zhang [view email][v1] Tue, 16 Apr 2024 10:04:20 GMT (6kb)
[v2] Thu, 18 Apr 2024 03:08:45 GMT (6kb)
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