Periodic homogenization of convolution type operators with heavy tails

The paper deals with periodic homogenization of nonlocal symmetric convolution type operators in $L^2({\mathbb{R}}^d)$, whose kernel is the product of a density that belongs to the domain of attraction of an $\alpha$-stable law and a rapidly oscillating positive periodic function. Assuming that the local oscillation of the said density satisfies a proper upper bound at infinity, we prove homogenization result for the studied family of operators.