Generalized Evans–Krylov and Schauder type estimates for nonlocal fully nonlinear equations with rough kernels of variable orders

We establish the generalized Evans–Krylov and Schauder type estimates for nonlocal fully nonlinear elliptic equations with rough kernels of variable orders. In contrast to fractional Laplacian operators having a fixed order differentiability ??(0,2), under consideration have orders differentiability. Since is not characterized by single number, we consider function ? describing differentiability, which allowed oscillate between two functions r?1 r?2 some 0<?1??2<2. By introducing Hölder spaces, provide C?? that generalizes standard C?+? estimates.