In interference tolerance based spectrum sharing systems, primary receivers (PRs) are protected by a predefined peak or average interference power constraint. To implement such systems, cognitive radio (CR) transmitters are required to adjust their transmit power so that the interference power received at the PR receivers is kept below the threshold value. Hence, a CR-transmitter requires knowledge of its channel and the primary receiver in order to allocate the transmit power. In practice, it is impossible or very difficult for a CR transmitter to have perfect knowledge of this channel state information (CSI). In this paper, we investigate the impact of imperfect knowledge of this CSI on the performances of both a primary and cognitive radio network. For fixed transmit power, average interference power (AIP) constraint can be maintained through knowledge of the channel distribution information. To maintain the peak interference power (PIP) constraint, on the other hand, the CR-transmitter requires the instantaneous CSI of its channel with the primary receiver. First, we show that, compared to the PIP constraint with perfect CSI, the AIP constraint is advantageous for primary users but not for CR users. Then, we consider a PIP constraint with imperfect CSI at the CR-transmitter. We show that inaccuracy in CSI reduces the interference at the PR-receivers that is caused by the CR-transmitter. Consequently the proposed schemes improve the capacity of the primary links. Contrarily, the capacities of the CR links significantly degrade due to the inaccuracy in CSI.