Privalov定理的一个推广

A generalization of Privalov theorem

把Hlder空间上的Privalov定理推广到LPS(D)空间上,证明当跳跃函数f(t)∈LPS∩LP时,分区解析函数F(z)=1/2πi∫Df(t)/t-zdt,zD的内部分支属于Besov空间,而F(z)在边界两边的正负边值F+(t)、F-(t)以及f(t)的奇异积分(SF)(t)均属于LPS(D)空间.

In this paper,the classic Privalov theorem in H？lder spaces was extended to the case of LPS（D）. It was proved that if the leap data f（ t）∈LP（D）∩LPS（D）,the inner exponent of the sectional analytic function F（ z）= 12πi∫D f（ t）t -zdt,zD belongs to the Basov space. Moreover,F＋（ t）、F-（ t）the boundary values of F（ z）on both sides ofD and（ SF）（ t）,the singular integral of f（ t）belong to LPS（D）.