Harmonic analysis for resistance forms
Harmonic analysis for resistance forms
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DOI：
10.1016/s0022-1236(02)00149-0
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发表时间：
2003-11
影响因子：
1.7
通讯作者：
Jun Kigami
中科院分区：
文献类型：
--
作者：
Jun Kigami
本文利用有效电阻和调和函数定义了电阻形式的格林函数。然后证明了格林函数和调和函数关于阻力度规一致Lipschitz连续。利用这一事实，我们构造了格林算子和(测值)拉普拉斯算子。拉普拉斯函数的区域是一致Lipschitz连续函数的子集，而阻力形式的区域一般由一致1/2-Hölder连续函数组成。
In this paper, we define the Green functions for a resistance form by using effective resistance and harmonic functions. Then the Green functions and harmonic functions are shown to be uniformly Lipschitz continuous with respect to the resistance metric. Making use of this fact, we construct the Green operator and the (measure valued) Laplacian. The domain of the Laplacian is shown to be a subset of uniformly Lipschitz continuous functions while the domain of the resistance form in general consists of uniformly 1/2-Hölder continuous functions.