Abstract: 

Consider manifold $\mathcal{M}=(\mathbb{R}^{n_1}\times \mathcal{M}_1) \# \dots \# (\mathbb{R}^{n_l}\times \mathcal{M}_l)$, we prove that the Reverse Riesz transform is bounded in all $L^p$ spaces. We then apply the same idea to the one dimensional model and obtain a similar result. Our method based on the parametrix construction and the boundedness of Riesz transform results obtained Hassell and Sikora.