Harmonic Functions in Upper Half Space

作者：Pan, Guo-Shuang^*; Qiao, Lei; Deng, Guan-Tie

来源：Bulletin of the Belgian Mathematical Society Simon Stevin, 2012, 19(4): 675-681.

DOI：10.36045/bbms/1353695908

• Harmonic function
• Integral Representation
• Half space

In this paper, we prove that if the positive part u(+)(x) of a harmonic function u(x) in the upper half space satisfies a fast growing condition, then its negative part u(-)(x) can also be dominated by a similar growing condition. Meanwhile, u (x) can be represented in terms of the modified Poisson integral and a harmonic function vanishing on the boundary.

• 单位
  北京师范大学; 河南财经政法大学