Vision Transformer (ViT) attains state-of-the-art performance in visual recognition, and the variant, Local Vision Transformer, makes further improvements. The major component in Local Vision Transformer, local attention, performs the attention separately over small local windows. We rephrase local attention as a channel-wise locally-connected layer and analyze it from two network regularization manners, sparse connectivity and weight sharing, as well as dynamic weight computation. We point out that local attention resembles depth-wise convolution and its dynamic variants in sparse connectivity: there is no connection across channels, and each position is connected to the positions within a small local window. The main differences lie in (i) weight sharing - depth-wise convolution shares connection weights (kernel weights) across spatial positions and attention shares the connection weights across channels, and (ii) dynamic weight computation manners - local attention is based on dot-products between pairwise positions in the local window, and dynamic convolution is based on linear projections conducted on the center representation or the globally pooled representation. The connection between local attention and dynamic depth-wise convolution is empirically verified by the ablation study about weight sharing and dynamic weight computation in Local Vision Transformer and (dynamic) depth-wise convolution. We empirically observe that the models based on depth-wise convolution and the dynamic variants with lower computation complexity perform on-par with or slightly better than Swin Transformer, an instance of Local Vision Transformer, for ImageNet classification, COCO object detection and ADE semantic segmentation. Code is available at https://github.com/Atten4Vis/DemystifyLocalViT.