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arXiv · 1302.0146

Boundedness of maximal functions on non-doubling manifolds with ends

Xuan Thinh Duong·Ji Li·Adam Sikora
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Abstract

Let $M$ be a manifold with ends constructed in \cite{GS} and $\Delta$ be the Laplace-Beltrami operator on $M$. In this note, we show the weak type $(1,1)$ and $L^p$ boundedness of the Hardy-Littlewood maximal function and of the maximal function associated with the heat semigroup $\M_\Delta f(x)=\sup_{t> 0} |\exp (-t\Delta)f(x)| $ on $L^p(M)$ for $1 < p \le \infty$. The significance of these results comes from the fact that $M$ does not satisfies the doubling condition.

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Xuan Thinh Duong, Ji Li, Adam Sikora. 2013-02-01. Boundedness of maximal functions on non-doubling manifolds with ends. https://arxiv.org/abs/1302.0146

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