混合范数空间与面积积分

MIXED NORM SPACES AND AREA INTEGRALS

研究了混合范数空间H( p ,q ,α) 中解析函数 f的面积积分Ar( f) 和Ar(t ,θ ,f)的增长性 ,对 p的不同取值 ,分别用Ar( f)和Ar(t ,θ ,f)给出了f∈H ( p ,q ,α)的充分条件和必要条件 .对D上的面积平均 j叶函数族 ,给出了充要条件 .结果推广了F .Holland ,J .B .Twomey和S .

In this paper we study the growth of area integrals Ar(t,θ,f) and Ar(f) of analytic function f in the mixed norm space H(p,q,α) .For different p ,we give a necessary condition and a sufficient condition for an analytic function f such that f∈H(p,q,α) by area integrals Ar(t,θ,f) and Ar(f) .In particular,for f∈S and all p>0 ,we give a necessary and sufficient condition for f∈H(p,q,α) .These results generalize the main theorems of F .Holland,J.B.Twomey and S.Yamashita.