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In this paper, the problem of wireless resource management in broadband cognitive OFDMA networks is addressed. Our objective is to maximize multiple cognitive users' weighted rate sum by jointly adjusting their rate, frequency, and power resource, under the constraints of multiple primary users' interference temperatures. First, we formulate the studied problem as a nonlinear and non-convex optimization problem. Secondly, we analyze this problem, and propose a centralized algorithm based on Lagrangian duality theory to solve it, which can be proved to be optimal and have polynomial time complexities. Finally, we show that this centralized algorithm can be distributively implemented by introducing the idea of virtual clock, and the distributed algorithm can be interpreted as an interesting distributed negotiated secondary market approach. We believe that our work will provide a good reference for the emerging cognitive network protocol design.