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The integrated terrestrial satellite networks (ITSNs) have been deemed as a promising solution to ubiquitous Internet access anytime and anywhere. In this paper, we investigate the spectrum sharing problem in ITSN, in particular focusing on the downlink transmission of the satellite network, which adopts the framing structure for the satellite users (SUs). We model the interference from both terrestrial downlink and uplink transmissions to SUs according to the beamforming techniques. For the terrestrial downlink transmission, we assume that terrestrial users (TUs) are served cooperatively by multiple small base stations (SBSs) via joint beamforming, while the virtual multiple access channel (VMAC) scheme is adopted for the terrestrial uplink transmission. We propose the optimization framework by jointly considering the terrestrial beamformer design and satellite user scheduling to maximize the sum rate of all users. The optimization problems are decomposed into three sub-problems: satellite user scheduling, terrestrial beamformer design, and time slot allocation, which are solved by deep clustering, second-order cone programming (SOCP) (or fractional programming (FP)), and linear programming, respectively. Then, an alternating iterative algorithm is designed to obtain the optimal solution. Simulation results are provided to demonstrate the effectiveness of the proposed algorithm in multiple cases.