Sharp quantitative stability estimates for critical points of fractional Sobolev inequalities

TL;DR

This paper develops a unified method to establish precise stability estimates for critical points of fractional Sobolev inequalities across the entire range of fractional orders, enhancing understanding of their stability properties.

Contribution

It introduces a unified approach based on integral representations to derive sharp quantitative stability estimates for fractional Sobolev inequalities.

Findings

Established sharp stability estimates for fractional Sobolev critical points

Unified approach applicable for all s in (0, n/2)

Improved understanding of stability in fractional Sobolev embeddings

Abstract

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