On the stability of a version of nonlocal Sobolev inequality

In this paper, we investigate the stability of the corresponding nonlocal Sobolev inequality [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is the best constant. More specifically, by utilizing the non-degenerate property, we will give the remainder term which is proportional to the quadratic distance.