C^n中Cauchy-Stieltjes积分及其乘子的性质

Properties of Cauchy-Stieltjes Integrals and Their Multipliers

讨论了n维复空间Cn中Cauchy-Stieltjes积分Fnp及其乘子Mnp的一些性质。通过对Mnp中函数f的径向导数Rf(z)的积分平均估计,证明了Mnp中的函数f是有界的。讨论了同一测度在不同乘子空间的积分之间的联系,从而得到Fnp的一个遗传性质。利用Cn中Dirichlet空间Dnq范数的积分表示证明了Fnp与Dnq的包含关系。

Some properties of Cauchy-Stieltjes integrals and their multipliers on the n-dimensional complex space are studied . It is proved that the function is bounded using estimates of integral means of radial derivatives for each. The connections of both integrals in the different multiplier space with the same measure are discussed. A result about hereditary property of Cauchy-Stieltjes integrals is obtained. The contained relations between Fpn and Dqn is also proved by using the integral representation of the norm of the Dirichlet space on.