Outside lab window I observed a female sharp-shinned hawk patrolling around cattle barn for sparrows. She landed in locust tree and a family of bluejays (~6) sassed her from an adjacent tree. Then the resident female American kestrel came in and did a display around with all her feathers spread out as she flew around the larger sharp-shinned. The kestrel landed about 15 feet away in same tree and continued with displaying. Then the sharp-shinned gave chase pursuing the smaller kestrel all over place in tight circles for about 30 seconds. The sharp-shinned then returned to her perch and kestrel went to tree with bluejays. Kestrel continued display at sharp-shinned as bluejays mobbed her and made short approaches towards the sharp-shinned as if mustering courage to attack it. After a couple more minutes the sharp-shinned flew away. I wish was close enough to hear sounds made between the two raptors.