非紧致型秩一黎曼对称空间上的球极大算子
Spherical maximal operators on rank one Riemannian symmetric spaces of noncompact type
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中文总结 AI 辅助
本文推广球极大算子至非紧致秩一黎曼对称空间，给出$L^p$有界性的充分与必要条件，并在$1<p\leq2$时确定实数$\mu$的精确范围。
中文摘要 AI 辅助
球极大算子（阶为$\mu$）由El Kohen在实双曲空间背景下引入，并研究了其$L^p$有界性。本文将这一概念推广到非紧致型的秩一黎曼对称空间。我们建立了参数$\mu$的充分条件，使得相应的球极大算子在$1<p\leq\infty$上对$L^p$有界。当$\mu$为实数且$1<p<\infty$时，我们还得到了$L^p$有界性的必要条件。特别地，对于$1<p\leq2$，必要条件与充分条件一致，从而在此范围内给出了实数$\mu$的精确范围。
英文摘要
The spherical maximal operator of order $μ$ was introduced by El Kohen in the setting of real hyperbolic spaces, where its $L^p$-boundedness properties were studied. In this paper, we extend this notion to rank-one Riemannian symmetric spaces of noncompact type. We establish sufficient conditions on the parameter $μ$ for the corresponding spherical maximal operator to be bounded on $L^p$ for $1<p\leq\infty$. We also obtain a necessary condition for $L^p$-boundedness when $μ$ is real and $1<p<\infty$. In particular, for $1<p\leq2$, the necessary condition agrees with the sufficient condition, yielding the sharp range of real $μ$ in this regime.
发表机构
- INDIAN INSTITUTE OF TECHNOLOGY BOMBAY（印度理工学院孟买分校）
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