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arXiv · 2211.11433

Riesz transform on manifolds with ends of different volume growth for $1<p<2$

Renjin Jiang·Hongquan Li·Haibo Lin
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Abstract

Let $M_1$, $\cdots$, $M_\ell$ be complete, connected and non-collapsed manifolds of the same dimension, where $2\le \ell\in\mathbb{N}$, and suppose that each $M_i$ satisfies a doubling condition and a Gaussian upper bound for the heat kernel. If each manifold $M_i$ has volume growth either bigger than two or equal to two, then we show that the Riesz transform $\nabla \L^{-1/2}$ is bounded on $L^p(M)$ for each $1<p<2$ on the gluing manifold $M=M_1\#M_2\#\cdots \# M_\ell$.

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Renjin Jiang, Hongquan Li, Haibo Lin. 2022-11-21. Riesz transform on manifolds with ends of different volume growth for $1<p<2$. https://arxiv.org/abs/2211.11433

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