$$W^{\sigma ,p}$$ estimates are studied for a class of fully nonlinear integro-differential equations order $$\sigma $$ , which analogues $$W^{2,p}$$ by Caffarelli. We also present Aleksandrov-Bakelman-Pucci maximum principles, improvements proved Guillen-Schwab, depending only on $$L^p$$ norms inhomogeneous terms.
