During the last decade we have seen an explosive growth in the deployment of wireless networks in unlicensed frequency bands, mainly driven by the great success of the IEEE 802.11 standard. In addition to its traditional last-hop usage, it has also been widely employed for Internet access infrastructure such as wireless mesh networks (WMNs). A problem that is envisioned in the near future is the spectrum scarcity, which could be a serious threat to cope with the ever increasing demand. Regulators are aware about this problem and they have already started to look for more available spectrum. One of the possibilities that has emerged is to allow secondary assignments in licensed bands, based on the recent cognitive radio networks (CRNs) paradigm. In this context, we focus our work in the analysis of optimum spectrum allocation mechanisms for a cognitive wireless multihop mesh network. We introduce a stochastic model to formulate the problem, considering primary users activity and a periodically scheduled assignment scheme. To solve the problem we propose a novel robust solution, for which we develop a decentralized algorithm implementation. Furthermore, we evaluate our proposal through extensive simulations, showing for instance its superiority compared with an expectation based approach.