Global weak Morrey estimates for some Ultraparabolic operators of Kolmogorov-Fokker-Planck type
Bull. Korean Math. Soc. 2014 Vol. 51, No. 5, 1241-1257
Printed September 30, 2014
Xiaojing Feng, Pengcheng Niu, and Maochun Zhu
Shanxi University, Northwestern Polytechnical University, Beijing Normal University
Abstract : We consider a class of hypoelliptic operators of the following type $$L=\sum^{p_0}_{i,j=1}a_{ij}\partial^2_{x_ix_j}+\sum^{N}_{i,j=1}b_{ij}x_i\partial_{x_j}-\partial_t,$$ where $(a_{ij}),\ (b_{ij})$ are constant matrices and $(a_{ij})$ is symmetric positive definite on ${\mathbb R}^{p_0}\ (p_0\leqslant N)$. By establishing global Morrey estimates of singular integral on the homogenous space and the relation between Morrey space and weak Morrey space, we obtain the global weak Morrey estimates of the operator $L$ on the whole space ${\mathbb R}^{N+1}$.
Keywords : ultraparabolic operators, weak Morrey estimates, homogeneous type space
MSC numbers : 35R05, 35B45, 42B20
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