ON THE LOWER BOUND FOR A CLASS OF HARMONIC FUNCTIONS IN THE HALF SPACE

作者：Zhang Yanhui^*; Deng Guantie; Kou, Kit Ian

来源：Acta Mathematica Scientia, 2012, 32(4): 1487-1494.

• harmonic function
• Carleman's formula
• Nevanlinna's representation for half sphere
• lower bound

The main objective is to derive a lower bound from an upper one for harmonic functions in the half space, which extends a result of B. Y. Levin from dimension 2 to dimension n >= 2. To this end, we first generalize the Carleman's formula for harmonic functions in the half plane to higher dimensional half space, and then establish a Nevanlinna's representation for harmonic functions in the half sphere by using Hormander's theorem.

• 单位
  北京师范大学; 北京工商大学