Hypoellipticity and parabolic hypoellipticity of nonlocal operators under Hörmander's condition
Hypoellipticity and parabolic hypoellipticity of nonlocal operators under Hörmander's condition
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Hörmander 条件下非局部算子的亚椭圆性和抛物线亚椭圆性
DOI：
10.1007/s11118-022-09997-6
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发表时间：
--
影响因子：
1.1
通讯作者：
Hua Zhang
中科院分区：
文献类型：
--
作者：
Jiagang Ren;Hua Zhang
本文证明了非局部算子在Hörmander条件下的亚椭圆性和抛物亚椭圆性。证明中的一个关键步骤是获得与这些算子相关的过程的密度的非对角小时间估计。为此，我们使用一个新版本的Malliavin演算的泊松空间，即借给粒子的方法，最近开发的Bouleau和丹尼斯。
In this paper, we prove the hypoellipticity and parabolic hypoellipticity of nonlocal operators under Hörmander’s condition. One key step in the proof is to obtain an off-diagonal small time estimate of the densities of the processes associated to these operators. To this end, we use a new version of Malliavin calculus on the Poisson space, namely the lent particle method, recently developed by Bouleau and Denis.