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Advanced recommender systems usually involve multiple domains (such as scenarios or categories) for various marketing strategies, and users interact with them to satisfy diverse demands. The goal of multi-domain recommendation (MDR) is to improve the recommendation performance of all domains simultaneously. Conventional graph neural network based methods usually deal with each domain separately, or train a shared model to serve all domains. The former fails to leverage users' cross-domain behaviors, making the behavior sparseness issue a great obstacle. The latter learns shared user representation with respect to all domains, which neglects users' domain-specific preferences. In this paper we propose $\mathsf{H^3Trans}$, a hierarchical hypergraph network based correlative preference transfer framework for MDR, which represents multi-domain user-item interactions into a unified graph to help preference transfer. $\mathsf{H^3Trans}$ incorporates two hyperedge-based modules, namely dynamic item transfer (Hyper-I) and adaptive user aggregation (Hyper-U). Hyper-I extracts correlative information from multi-domain user-item feedbacks for eliminating domain discrepancy of item representations. Hyper-U aggregates users' scattered preferences in multiple domains and further exploits the high-order (not only pair-wise) connections to improve user representations. Experiments on both public and production datasets verify the superiority of $\mathsf{H^3Trans}$ for MDR.