# Quantitative truncation estimates for fractional Hardy-Sobolev optimizers

## TL;DR

This paper provides quantitative stability estimates for truncations of functions concentrating at the origin, specifically applied to fractional Hardy-Sobolev optimizers, aiding the analysis of critical fractional equations.

## Contribution

It introduces new quantitative stability estimates for truncations in the context of fractional Hardy-Sobolev optimizers, enhancing understanding of their stability properties.

## Key findings

- Quantitative truncation estimates for fractional Hardy-Sobolev optimizers.
- Application of stability estimates to critical fractional p-q equations.
- Insight into the stability behavior of functions concentrating at the origin.

## Abstract

The general stability problem of truncations for a family of functions concentrating mass at the origin is described and a concrete example in the framework of entire optimizers for the fractional Hardy-Sobolev inequality is given. In this short note we point out some quantitative stability estimates, useful in dealing with critical $p-q$ fractional equations.