Sharp Quantitative Stability Estimates for Critical Points of Fractional Sobolev Inequalities

Abstract

By developing a unified approach based on integral representations, we establish sharp quantitative stability estimates of the fractional and higher-order Sobolev inequalities, induced by the embedding $\dot{H}<^>{s}(\mathbb{R}<^>{n}) \hookrightarrow L<^>{2n \over n-2s}(\mathbb{R}<^>{n})$ for any $s \in (0,\frac{n}{2})$, in the critical point setting.

By developing a unified approach based on integral representations, we establish sharp quantitative stability estimates of the fractional and higher-order Sobolev inequalities, induced by the embedding H˙ s(Rn) → L 2n n−2s (Rn) for any s ∈ (0, n 2 ), in the critical point setting.