Hardy spaces and divergence operators on strongly Lipschitz domains of Rn
Hardy spaces and divergence operators on strongly Lipschitz domains of Rn
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DOI：
10.1016/s0022-1236(03)00059-4
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发表时间：
2002-01
影响因子：
1.7
通讯作者：
P. Auscher;E. Russ
中科院分区：
文献类型：
--
作者：
P. Auscher;E. Russ
设Ω是Rn的强Lipschitz整环.考虑一个椭圆二阶发散算子L（包括一个关于Ω的边界条件），通过将函数f的扩张的非切极大函数加到L的Poisson半群中来定义一个哈代空间，使L在L1中.在L上适当的假设下，当Ω= Rn时，我们将这个极大哈代空间与H1（Rn），Dirichlet边界条件下与Hr 1（Ω），Neumann边界条件下与Hz 1（Ω）相一致.
Let Ω be a strongly Lipschitz domain of Rn. Consider an elliptic second-order divergence operator L (including a boundary condition on ∂Ω ) and define a Hardy space by imposing the non-tangential maximal function of the extension of a function f via the Poisson semigroup for L to be in L1. Under suitable assumptions on L, we identify this maximal Hardy space with H1( Rn) if Ω= Rn, with Hr1(Ω) under the Dirichlet boundary condition, and with Hz1(Ω) under the Neumann boundary condition.