The robotics community has been paying more attention to coverage functions due to their variant applications (e.g., spatial search and mapping, etc.). Due to their submodularity, greedy algorithms can find solutions with theoretical guarantees for maximizing coverage problems even if these problems are NP-hard. However, learning coverage functions is still a challenging problem since the number of function outcome for N sets is 2 N. Moreover, transfer learning of coverage functions is unexplored. This research focuses on the transfer learning of coverage functions via utilizing the invariant properties in the Fourier domain. The proposed algorithms based on these properties can construct Fourier support for learning coverage functions. Experiments conducted with these algorithms show that the robot can learn the coverage functions using less samples than the prior learning approaches in different environments. Experiments also show that the lossless compression rate of the proposed algorithms is up to 40 billion.