The generalized Cesàro operator on the unit polydisk. (Q1432843)

Let \(D_n\) be the unit polydisk in \(\mathbb{C}^n\). The main purpose of the present paper is to prove the boundedness of the generalized Cesàro operators \(C^{\overline\gamma}\) on the Hardy spaces \(H^p(D_n)\) and also on the generalized Bergman spaces \(A^{p,q}_{\overline\mu}(D_n)\), where \(0< p\), \(q<\infty\) and \(\overline\gamma= (\gamma_1,\dots, \gamma_n)\) with \(\text{Re}(\gamma_j)> 1\), \(j= 1,\dots, n\). Here \(\overline\mu= (\mu_1,\dots, \mu_n)\) and each \(\mu_j\) is a positive Borel measure on the interval \([0,1)\). Also, in this interesting paper, the authors present a class of invariant spaces under the action of the generalized Cesàro operators.