## View abstract

### Session S38 - Geometric Potential Analysis

Friday, July 16, 20:10 ~ 20:40 UTC-3

## The fractional Laplacian and fractional gradient operators

### Liguang Liu

We will talk about some recent results related to the fractional Laplacian $\nabla^s_+=(-\Delta)^{\frac s2}$ and the fractional gradient $\nabla^s_-=\nabla (-\Delta)^{\frac {s-1}{2}}$, including also some optimal inequalities of type Hardy-Rellich/Adams-Moser/Morrey-Sobolev, and regularity of the distributional solutions to the dual equations $[\nabla^s_\pm]^\ast u=f$.