This study presents a lightweight dual-domain super-resolution network (DDSRNet) that combines Spatial-Net with the discrete wavelet transform (DWT). Specifically, our proposed model comprises three main components: (1) a shallow feature extraction module, termed Spatial-Net, which performs residual learning and bilinear interpolation; (2) a low-frequency enhancement branch based on the DWT that refines coarse image structures; and (3) a shared high-frequency refinement branch that simultaneously enhances the LH (horizontal), HL (vertical), and HH (diagonal) wavelet subbands using a single CNN with shared weights. As a result, the DWT enables subband decomposition, while the inverse DWT reconstructs the final high-resolution output. By doing so, the integration of spatial- and frequency-domain learning enables DDSRNet to achieve highly competitive performance with low computational cost on three hyperspectral image datasets, demonstrating its effectiveness for hyperspectral image super-resolution.