  We prove Schauder estimates for a class of non-local elliptic operators with
kernel $K(y)=a(y)/|y|^{d+\sigma}$ and either Dini or H\"older continuous data.
Here $0 < \sigma < 2$ is a constant and $a$ is a bounded measurable function,
which is not necessarily to be homogeneous, regular, or symmetric. As an
application, we prove that the operators give isomorphisms between the
Lipschitz--Zygmund spaces $\Lambda^{\alpha+\sigma}$ and $\Lambda^\alpha$ for
any $\alpha>0$. Several local estimates and an extension to operators with
kernels $K(x,y)$ are also discussed.
