UAV small object detection has essential applications in the military, search and rescue, and smart cities, providing critical support for target recognition in complex environments. However, the existing UAV small object detection models usually have many parameters and high computational complexity, limiting their deployment and application in practical scenarios to some extent. In this study, we propose a UAV detector with Lightweight Multidimensional Feature Network (LMF-UAV), aiming to reduce the number of parameters and computation of the model while guaranteeing accuracy, which constructs the Lightweight Multidimensional Feature Network (LMF-Net) for lightweight feature extraction, and Efficient Expressive Network (EENet) for efficient feature fusion. Neural architecture search utilizes the Dual-branch Cross-stage Universal Inverted Bottleneck to enable the network to select the most suitable structure at different layers according to requirements, thereby improving the computational efficiency of LMF-Net while maintaining performance. EENet uses the Channel-wise Partial Convolution Stage to reduce redundant computation and memory access and fuse spatial features more effectively. First, LMF-Net extracts features from the images collected by UAV and obtains three multi-scale feature maps. Second, EENet performs feature fusion on three feature maps of different scales to obtain three feature representatives. Finally, the decoupled head detects the feature map and outputs the final result. The bounding box regression loss function uses Wasserstein distance to evaluate box similarity and enhance the model's sensitivity to small targets. The experimental results demonstrate that on the VisDrone dataset, mAP50-95 of LMF-UAV reaches 24.6%, while parameters are only 14.7M, FLOPs are only 61.8G, showing a good balance between performance and efficiency.