Bergman空间到Dirichlet空间的Cesàro算子

Cesàro Operator From Bergman Space to Dirichlet Space

讨论了在Cn中单位球上Bergman空间到Dirichlet空间的Cesàro算子的有界性和紧性,得出当α,β>-1,0<p<q<∞时,Bergman空间Aαp到Dirichlet空间Dβq的加权Cesàro算子T为有界算子和紧算子的充要条件。

The boundedness and compactness for the Cesaro operator Tψ, from Bergman space Ap to Dirichlet space Dβq are discussed on the unit ball of Cn. It can obtain the bounded or compact sufficient and necessary conditions for the extended Cesaro operator Tψ, from Bergman spaces Ap to Dirichletspaces Dβq if α,β 〉-1, 0〈p≤q〈∞.