On boundedness of the generalized Riesz potential in local Morrey type spaces

$$ \left(I_{\rho(\cdot)}f\right)(x) = \int_{\mathbb{R}^{n}}^{}\rho(|x-y|)f(y) dy,\ x\in \mathbb{R}^{n}, $$
under certain assumptions on the kernel $\rho$.