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

Abstract : 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
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Submitted on : Tuesday, May 16, 2017 - 1:57:34 PM
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  • HAL Id : hal-01349567, version 2
  • ARXIV : 1607.08718

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L. Huang, S. Menozzi, E. Priola. $L^$p Estimates For Degenerate Non-Local Kolmogorov Operators. Journal de Mathématiques Pures et Appliquées, Elsevier, 2017, ⟨https://doi.org/10.1016/j.matpur.2017.12.008⟩. ⟨hal-01349567v2⟩

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