We consider the problem of decentralized multiagent environmental learning through maximizing the joint information gain among a team of agents. Inspired by subsea applications where bandwidth is severely limited, we explicitly consider the challenge of restricted communication between agents. The environment is modeled as a Gaussian process (GP), and the global information gain maximization problem in a GP is a set-valued optimization problem involving all agents' locally acquired data. We develop a decentralized method to solve it based on decomposition of information gain and exchange of limited subsets of data between agents. A key technical novelty of our approach is that we formulate the incentives for information exchange among agents as a submodular set optimization problem in terms of the log-determinant of their local covariance matrices. Numerical experiments on real-world data demonstrate the ability of our algorithm to explore trade-off between objectives. In particular, we demonstrate favorable performance on mapping problems where both decentralized information gathering and limited information exchange are essential.