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

Let $M_1$, $\cdots$, $M_{\mathrm{\ell }}$ be complete, connected and non-collapsed manifolds of the same dimension, where $2\le \mathrm{\ell }\in \mathbb{N}$, 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 $\mathrm{\nabla }{\text{Ł}}^{-1\mathrm{/}2}$ is bounded on $L^p(M)$ for each $1<p<2$ on the gluing manifold $M=M_1\mathrm{\#}{M}_2\mathrm{\#}\cdots \mathrm{\#}{M}_{\mathrm{\ell }}$.