In this work, we address the problem of optimal spectrum management in continuous frequency domain in multiuser interference channels. The objective is to maximize the weighted sum of user capacities. Our main results are as follows: (i) For frequency-selective channels, we prove that in an optimal solution, each user uses maximum power; this result also generalizes to the cases where the objective is to maximize the weighted product (i.e., proportional fairness) of user capacities. (ii) For the special case of two users in flat channels, we solve the problem optimally.