Seminar on theory of function spaces

Nonlocal gradient potential estimates

We consider nonlocal equations of order larger than one with measure data and present pointwise bounds of the gradient in terms of Riesz potentials. These gradient potential estimates lead to fine regularity results in many commonly used function spaces, in the sense that "passing through potentials" enables us to detect finer scales that are difficult to reach by more traditional methods. The talk is based on joint work with Tuomo Kuusi and Yannick Sire.