$L^$p Estimates For Degenerate Non-Local Kolmogorov Operators

L. Huang (1) , S. Menozzi (2, 3) , E. Priola (4)

1 Michigan State University [East Lansing]
2 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry
3 Higher School of Economics
4 Dipartimento di Matematica "Giuseppe Peano" [Torino]

Let $z = (x,y) \in {\mathbb R}^d \times {\mathbb R}^{N-d}$, with $1 \le d < N$. We prove a priori estimates of the following type : $$ \|\Delta_{x}^{\frac \alpha 2} v \|_{L^p({\mathbb R}^N)} \le c_p \Big \| L_{x } v + \sum_{i,j=1}^{N}a_{ij}z_{i}\partial_{z_{j}} v \Big \|_{L^p({\mathbb R}^N)}, \;\; 1

Mots clés: Degenerate non local operators; Calderon-Zygmund estimates; L^p estimates

Domaines: Equations aux dérivées partielles [math.AP]; Probabilités [math.PR]

L. Huang, S. Menozzi, E. Priola. $L^$p Estimates For Degenerate Non-Local Kolmogorov Operators. Journal de Mathématiques Pures et Appliquées, 2017. ⟨hal-01349567v2⟩