Pan-sharpening is a super-resolution problem that essentially relies on spectra fusion of panchromatic (PAN) images and low-resolution multi-spectral (LRMS) images. The previous methods have validated the effectiveness of information fusion in the Fourier space of the whole image. However, they haven't fully explored the Fourier relationships at different hierarchies between PAN and LRMS images. To this end, we propose a Hierarchical Frequency Integration Network (HFIN) to facilitate hierarchical Fourier information integration for pan-sharpening. Specifically, our network consists of two designs: information stratification and information integration. For information stratification, we hierarchically decompose PAN and LRMS information into spatial, global Fourier and local Fourier information, and fuse them independently. For information integration, the above hierarchical fused information is processed to further enhance their relationships and undergo comprehensive integration. Our method extend a new space for exploring the relationships of PAN and LRMS images, enhancing the integration of spatial-frequency information. Extensive experiments robustly validate the effectiveness of the proposed network, showcasing its superior performance compared to other state-of-the-art methods and generalization in real-world scenes and other fusion tasks as a general image fusion framework.