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In $L_2(\mathbb{R}^d)$, we consider a selfadjoint bounded operator ${\mathbbA}_\varepsilon$, $\varepsilon >0$, of the form $$ ({\mathbb A}_\varepsilon u)(\mathbf{x}) = \varepsilon^{-d-2} \int_{\mathbb{R}^d} a((\mathbf{x} -\mathbf{y} )/ \varepsilon ) \mu(\mathbf{x} /\varepsilon, \mathbf{y}/\varepsilon) \left( u(\mathbf{x}) - u(\mathbf{y}) \right)\, d\mathbf{y}. $$ Itis assumed that $a(\mathbf{x})$ is a nonnegative function of class$L_1(\mathbb{R}^d)$ such that \hbox{$a(-\mathbf{x}) = a(\mathbf{x})$} and$\mu(\mathbf{x},\mathbf{y})$ is $\mathbb{Z}^d$-periodic in each variable andsuch that $\mu(\mathbf{x},\mathbf{y}) = \mu(\mathbf{y},\mathbf{x})$ and $0<\mu_- \leqslant \mu(\mathbf{x},\mathbf{y}) \leqslant \mu_+< \infty$. Moreover,it is assumed that the moments $M_k (a)= \int_{\mathbb{R}^d} | \mathbf{x} |^ka(\mathbf{x})\,d\mathbf{x}$, $k=1,2,3,4,$ are finite. We obtain approximationof the resolvent $({\mathbb A}_\varepsilon + I)^{-1}$ for small $\varepsilon$in the operator norm on $L_2(\mathbb{R}^d)$ with error of order$O(\varepsilon^2)$.

Homogenization of nonlocal convolution type operators: Approximation for the resolvent with corrector