High-resolution fully digital transceivers are infeasible at millimeter-wave (mmWave) due to their increased power consumption, cost, and hardware complexity. The use of low-resolution converters is one possible solution to realize fully digital architectures at mmWave. In this paper, we consider a setting in which a fully digital base station with constant envelope quantized (CEQ) digital-to-analog converters on each radio frequency chain communicates with multiple single antenna users with individual signal-to-quantization-plus-interference-plus-noise ratio (SQINR) constraints over frequency selective channels. We first establish uplink downlink duality for the system with CEQ hardware constraints and OFDM-based transmission considered in this paper. Based on the uplink downlink duality principle, we present a solution to the multi-user multi-carrier beamforming and power allocation problem that maximizes the minimum SQINR over all users and sub-carriers. We then present a per sub-carrier version of the originally proposed solution that decouples all sub-carriers of the OFDM waveform resulting in smaller sub-problems that can be solved in a parallel manner. Our numerical results based on 3GPP channel models generated from Quadriga demonstrate improvements in terms of ergodic sum rate and ergodic minimum rate over state-of-the-art linear solutions. We also show improved performance over non-linear solutions in terms of the coded bit error rate with the increased flexibility of assigning individual user SQINRs built into the proposed framework.