This paper considers the problem of minimizing outage probabilities in the downlink of a multiuser, multicell orthogonal frequency division multiple access (OFDMA) cellular network with frequency selective fading, imperfect channel state information, and frequency hopping. The task is to determine the allocation of powers and sub carriers for users to ensure that the user outage probabilities are as low as possible. We formulate a min-max outage probability problem and solve it under the constraint that the transmit power spectrum at each base station is flat. In particular, we obtain a sub channel allocation algorithm that has complexity O(L log L) in L, the number of users in the cell. We also consider suboptimal but implementable approaches with and without the flat transmit power spectrum constraint.We conclude that the flat transmit spectrum approach has merit, and warrants further study.