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This paper studies the problem of robust downlink beamforming design in a multiuser multiple-input-single-output (MISO) cognitive radio network (CR-Net) in which multiple secondary users (SUs) coexist with multiple primary users (PUs) of a single-cell primary radio network (PR-Net). It is assumed that the channel-state information (CSI) for all relevant channels is imperfectly known, and the imperfectness of the CSI is modeled using a Euclidean ball-shaped uncertainty set. Our design objective is to minimize the transmit power of the SU-Transmitter (SU-Tx) while simultaneously achieving a lower bound on the received signal-to-interference-plus-noise ratio (SINR) for the SUs and imposing an upper limit on the interference power (IP) at the PUs. The design parameters at the SU-Tx are the beamforming weights, and the proposed methodology to solve the problem is based on the worst-case design scenario through which the performance metrics of the design are immune to variations in the channels. The original problem is a separable homogeneous quadratically constrained quadratic problem (QCQP), which is an NP-hard problem, even for uncertain CSI. We reformulate our original design problem to a relaxed semidefinite program (SDP) and then investigate three different approaches based on convex programming. Finally, simulation results are provided to validate the robustness of the proposed methods.