Image areas and BMO norms of analytic functions
Image areas and BMO norms of analytic functions
复制标题
DOI：
10.2996/kmj/1138037045
复制
发表时间：
1985
影响因子：
0.6
通讯作者：
Shōji Kobayashi
中科院分区：
文献类型：
--
作者：
Shōji Kobayashi
对于单位圆盘U中的解析函数f，若f(0)=0，则证明了H/h~2-面积{f(U)}中的等式成立的充要条件是f是内函数的常数倍。作为推论，证明了对于一般区域上的解析函数，其H~2范数的平方与其Dirichlet积分有界，且等式条件已成立
For an analytic function / in the unit disc U with /(0) = 0, the inequality H/H2 < - area {f(U)} is shown, where an equality occurs if and only if / is a constant multiple of an inner function. As a corollary, it is shown that for an analytic function in a general domain the square of its H2 norm is bounded by its Dirichlet integral, with the equality condition being settled