Difficult work question.

Please help. I am a professional, as is the woman I supervise, who joined our company several months ago. We are at similar levels but I am her supervisor. “Jane” has repeatedly expressed frustration via emails to me with copies to MY superiors that I am not helping her enough, that she was led to believe that I would be helping her advance more in her position, etc. She comes across as “entitled” and belligerent. I have spent time with her, showing her things and helped her, in a neutral manner. I have given her staff to help her, and she has treated them poorly as well. She continues to lash out via email and will interrupt me when I am seeing clients to ask non-urgent, demanding questions. I know we cannot control other people’s thoughts, feelings, or actions. I have tried to remain “curious,” but – as her supervisor – I must address this. What do you suggest? Thank you for your wisdom!