Dirichlet heat kernel estimates for fractional Laplacian under non-local perturbation

Zhen-Qing Chen, Ting Yang

For $d\ge 2$ and $0<\beta <\alpha <2$, consider a family of non-local operators ${\mathcal{L}}^b={\Delta }^{\alpha /2}+{\mathcal{S}}^b$ on ${\mathbb{R}}^d$, where $$ \mathcal{S}^{b}f(x):=\lim_{\varepsilon\to…