Equidistribution of holomorphic cusp forms on thin sets

We find some equidistribution results connected to restriction quantum unique ergodicity problem in this paper. We shows that \begin{align*} \frac{1}{|$\mathcal{B}$k|}\sum{f\in $\mathcal{B}$k} \int{R}y^{k}|f(z)|^{2}ψ(z) dμ_{R}(z)\to \frac{3}π\int_{R}ψ(z) dμ_{R}(z) \end{align*} where $R$ is some subset of $\mathbb{H}$, $\psi$ is a nice function relative to $R$, $d{\mu }_R(z)$ is a suitable measure on $R$, and ${\mathcal{B}}_k$ is an orthonormal basis of the cusp forms for group $\mathrm{\Gamma }$ with respect to weight $k$.