Bulletin of the Korean Mathematical Society (대한수학회보)

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GLOBAL WEAK MORREY ESTIMATES FOR SOME ULTRAPARABOLIC OPERATORS OF KOLMOGOROV-FOKKER-PLANCK TYPE

  • Feng, Xiaojing (Department of Applied Mathematics Key Laboratory of Space Applied Physics and Chemistry Ministry of Education Northwestern Polytechnical University, School of Mathematical Sciences Shanxi University) ;
  • Niu, Pengcheng (Department of Applied Mathematics Key Laboratory of Space Applied Physics and Chemistry Ministry of Education Northwestern Polytechnical University, School of Mathematical Sciences Beijing Normal University) ;
  • Zhu, Maochun (Department of Applied Mathematics Key Laboratory of Space Applied Physics and Chemistry Ministry of Education Northwestern Polytechnical University, School of Mathematical Sciences Beijing Normal University)
  • Received : 2011.03.28
  • Published : 2014.09.30
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Abstract

We consider a class of hypoelliptic operators of the following type $$L=\sum_{i,j=1}^{p_0}a_{ij}{\partial}^2_{x_ix_j}+\sum_{i,j=1}^{N}b_{ij}x_i{\partial}_{x_j}-{\partial}_t$$, 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 $\mathbb{R}^{N+1}$.

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References

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