|Aug 17, 2023
|Bielefeld University, Germany
We consider the non-local p-Laplacian with possible weights of VMO-type. We prove higher regularity of Calderon-Zygmund-type. We accomplish this by establishing precise pointwise bounds in terms of certain fractional sharp maximal functions. This approach is new already in the linear setting and enables us to deduce sharp regularity results also in borderline cases.