重调和函数的平均值性质(英文)

MEAN VALUE PROPERTIES OF PLURIHARMONIC FUNCTIONS~*

设Ω是 C^n 中的有界对称域,f=u+jv 是Ω上的全纯函数,f(0)∈R.记(?)_(p,q,α)=(?)(1-r)^(qα-1)M_p^(?)(r,f)dr(?)^(1/q).本文证明了(?)_(p,q,α),≤C(?)_(p,q,a)(0<p,q≤∞,α>0).

Let f=u+iv be holomorphic in bounded symmetric domainΩ(?)C^n,with f(0)real,‖f‖p,q,a={_0~1(1-r)^(qa-1)M_p^q(r,f)dr}^(1/q).We prove that‖f‖p,q,a,≤c‖u‖p,q,a for 0<p,q≤+∞,a>which completes the known results in[6].