Current event-based video reconstruction methods, limited to the spatial domain, face challenges in decoupling brightness and structural information, leading to exposure distortion, and in efficiently acquiring non-local information without relying on computationally expensive Transformer models. To address these issues, we propose the Deep Spatial-Frequency Unfolding Reconstruction Network (DSFURNet), which explores and utilizes knowledge in the frequency domain for event-based video reconstruction. Specifically, we construct a variational model and propose three regularization terms: a brightness regularization term approximated by Fourier amplitudes, a structural regularization term approximated by Fourier phases, and an initialization regularization term that converts event representations into initial video frames. Then, we design corresponding spatial-frequency domain approximation operators for each regularization term. Benefiting from the global nature of computations in the frequency domain, the designed approximation operators can integrate local spatial and global frequency information at a lower computational cost. Furthermore, we combine the learned knowledge of the three regularization terms and unfold the optimization algorithm into an iterative deep network. Through this approach, the pixel-level initialization regularization constraint and the frequency domain brightness and structural regularization constraints can continuously play a role during the testing process, achieving a gradual improvement in the quality of the reconstructed video frames. Compared to existing methods, our network significantly reduces the number of network parameters while improving evaluation metrics.