This document summarizes research on downlink beamforming and admission control for spectrum sharing cognitive radio systems. It discusses maximizing the number of admitted secondary links under interference and QoS constraints, as well as maximizing the sum throughput of admitted secondary links. An iterative algorithm based on geometric programming is proposed to solve the non-convex throughput maximization problem. Simulation results show a tradeoff between number of admitted links and secondary network throughput, but that enforcing QoS constraints does not significantly reduce throughput. The goal is to minimize secondary transmitter power while meeting SINR and interference limits.