On Schauder estimates for a class of nonlocal fully nonlinear parabolic equations

We obtain Schauder estimates for a class of concave fully nonlinear nonlocal parabolic equations of order $\sigma \in (0,2)$ with rough and non-symmetric kernels. As a application, we prove that the solution to a translation invariant equation with merely bounded data is $C^{\sigma }$ in $x$ variable and ${\mathrm{\Lambda }}^1$ in $t$ variable, where ${\mathrm{\Lambda }}^1$ is the Zygmund space.