Séminaire EDP-Analyse ICJ

# Reverse Riesz transforms in manifolds with (sub)gaussian estimates

## by Emmanuel Russ (IF, Université Grenoble Alpes)

Europe/Paris
Fokko (ICJ)

### Fokko

#### ICJ

Description

Let $(M,g)$ be a complete Riemannian manifold, $\Delta$ the Laplace Beltrami operator and $\nabla$ the gradient. We investigate the validity of the inequality $\left\Vert \Delta^{\frac 12}f\right\Vert_p\leq C \left\Vert \left\vert \nabla f\right\vert \right\Vert_p$, $1<p<\infty$, under various geometric assumptions. Some fractal-like situations will also be considered. This is joint work with Baptiste Devyver.