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

Renjin Jiang, Hongquan Li, Haibo Lin

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 doub…