real analysis – Another uniform estimation of an integral involving an Hölder function with derivative that is Hölder

Let $Omegasubsetmathbb{R}^n$, let $sin (1/2,1)$, let $uin C^{1,2s-1+epsilon}(Omega)$ such that: $u=0$ on $mathbb{R}^nsetminusOmega$, and: $uin C^{0,s}(mathbb{R}^n)$, is true that there exist a constant $C>0$, such that:
$$ int_{mathbb{R}^n}frac{|u(x)-u(y)|}{|x-y|^{n+2s}},dyleq C,qquadforall xinmathbb{R}^n.$$
Her $C>0$ does not depend to x.
Here $epsilon>0$ is small such that: $2s-1+epsilonin(0,1)$, and $C^{k,alpha}(A)$ is the space of $alpha$-Hölder functions whose derivative of order less than $kinmathbb{N}$ are $alpha$-Hölder on the open set $Asubsetmathbb{R}^n$. I have no idea on how to proceed, any help is appreciated.