We show that the fractional Sobolev inequality for the embedding ↪˝LN−s2N(RN), s∈(0,N) can be sharpened by
adding a remainder term proportional to the distance to the set of optimizers.
As a corollary, we derive the existence of a remainder term in the weak
LN−sN-norm for functions supported in a domain of finite measure.
Our results generalize earlier work for the non-fractional case where s is an
even integer.Comment: 13 page