We prove the attainability of the best constant in the fractional Hardy-Sobolev inequality with a boundary singularity for the spectral Dirichlet Laplacian. The main assumption is the average concavity of the boundary at the origin. A similar result has been proved earlier for the conventional Hardy-Sobolev inequality.

中文翻译：

---

分数阶Dirichlet拉普拉斯算子的分数Hardy-Sobolev不等式中最佳常数的可及性

我们证明了在谱Dirichlet Laplacian具有边界奇点的分数Hardy-Sobolev不等式中最佳常数的可实现性。主要假设是原点边界的平均凹度。对于传统的Hardy-Sobolev不等式，先前已经证明了类似的结果。