Integrating terrestrial and non-terrestrial networks has emerged as a promising paradigm to fulfill the constantly growing demand for connectivity, low transmission delay, and quality of services (QoS). This integration brings together the strengths of terrestrial and non-terrestrial networks, such as the reliability of terrestrial networks, broad coverage, and service continuity of non-terrestrial networks like low earth orbit (LEO) satellites. In this work, we study a data service maximization problem in an integrated terrestrial-non-terrestrial network (I-TNT) where the ground base stations (GBSs) and LEO satellites cooperatively serve the coexisting aerial users (AUs) and ground users (GUs). Then, by considering the spectrum scarcity, interference, and QoS requirements of the users, we jointly optimize the user association, AUE's trajectory, and power allocation. To tackle the formulated mixed-integer non-convex problem, we disintegrate it into two subproblems: 1) user association problem and 2) trajectory and power allocation problem. Since the user association problem is a binary integer programming problem, we use the standard convex optimization method to solve it. Meanwhile, the trajectory and power allocation problem is solved by the deep deterministic policy gradient (DDPG) method to cope with the problem's non-convexity and dynamic network environments. Then, the two subproblems are alternately solved by the proposed iterative algorithm. By comparing with the baselines in the existing literature, extensive simulations are conducted to evaluate the performance of the proposed framework.

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