半平面中的一类调和函数及其性质

A CLASS OF HARMONIC FUNCTIONS AND PROPERTIES IN HALF PLANE

利用半平面中修改的Poisson核,证明了如果R上一个σ—有限的Borel测度满足某些限制增长条件,则由半平面上修改的Poisson积分表示出来的函数收敛而且是一个调和函数,这一结果改进了半平面中调和函数的某些经典结果.

Using a property of the modified poisson kernel in a half plane, we prove that a function u （ z ） represented by modified Poisson integral with a Borel measure satisfying a slowly growing condition is convergent for any z∈C＋ and represents a harmonic function in C＋