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Cognitive radio can significantly improve the spectrum utilization by enabling secondary users (SUs) to opportunistically access the spectrum licensed to primary users (PUs). One practical yet challenging scenario is when both the PU occupancy and the channel fading change over time and exhibit temporal correlations. Little work has been done for simultaneously exploiting the temporal memory in both channel fading and PU occupancy for spectrum scheduling, and in particular, the scenario where PU occupancy presents a long temporal memory has been underexplored. In this work, we consider a cognitive radio network with multiple PUs and one SU, where a spectrum server is employed for scheduling the SU to transmit over one of the PU channels opportunistically. A primary goal is to understand the tradeoffs that arise from the intricate interactions between channel fading and PU occupancy, and the impact of the associated temporal memory. By casting the problem as a partially observable Markov decision process, we identify and illustrate a set of multi-tier tradeoffs that go beyond the classic "exploitation vs. exploration" tradeoff. We show that a simple greedy policy is optimal in some special cases. To build a deeper understanding of the tradeoffs, we further introduce a full-observation genie-aided system that helps in decomposing the tradeoffs in the original system into multiple layers, which we examine progressively. Numerical examples indicate that the optimal scheduler in the original system, with observation on the scheduled channel only, achieves a performance very close to the genie-aided system. In addition, the optimal policy in the original system significantly outperforms randomized scheduling, as well as a policy that explores memory in PU occupancy only, pointing to the advantages of jointly exploiting the temporal correlation structure in both channel fading and PU occupancy.