Lipschitz regularity of fractional $p$-Laplacian

In this article, we investigate the Hölder regularity of the fractional $p$-Laplace equation of the form $(-Δ_p)^s u=f$ where $p>1, s\in (0, 1)$ and $f\in L^\infty_{\rm loc}(Ω)$. Specifically, we prove that $u\in C^{0, γ_\circ}_{\rm loc}(Ω)$ for $γ_\circ=\min\{1, \frac{sp}{p-1}\}$, provided that $\f