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The non-uniformly distributed nature of the 3D dynamic point cloud (DPC) brings significant challenges to its high-efficient inter-frame compression. This paper proposes a novel 3D sparse convolution-based Deep Dynamic Point Cloud Compression (D-DPCC) network to compensate and compress the DPC geometry with 3D motion estimation and motion compensation in the feature space. In the proposed D-DPCC network, we design a {\it Multi-scale Motion Fusion} (MMF) module to accurately estimate the 3D optical flow between the feature representations of adjacent point cloud frames. Specifically, we utilize a 3D sparse convolution-based encoder to obtain the latent representation for motion estimation in the feature space and introduce the proposed MMF module for fused 3D motion embedding. Besides, for motion compensation, we propose a 3D {\it Adaptively Weighted Interpolation} (3DAWI) algorithm with a penalty coefficient to adaptively decrease the impact of distant neighbors. We compress the motion embedding and the residual with a lossy autoencoder-based network. To our knowledge, this paper is the first work proposing an end-to-end deep dynamic point cloud compression framework. The experimental result shows that the proposed D-DPCC framework achieves an average 76\% BD-Rate (Bjontegaard Delta Rate) gains against state-of-the-art Video-based Point Cloud Compression (V-PCC) v13 in inter mode.