## Taiwanese Journal of Mathematics

### THE GENERALIZED CESARO OPERATOR ON THE UNIT POLYDISK

#### Abstract

Let $D_n=\{(z_1,\dots, z_n)\in {\bf C}^n:\, |z_j|\lt 1,\,j=1,\dots,n\}$ be the unit polydisk in ${\bf C}^n$. The aim of this paper is to prove the boundedness of the generalized Ces\ aro operators ${\cal C}^{\vec\gamma}$ on $H^p(D_n)$ (Hardy) and ${\cal A}^{p,q}_{\vec \mu}(D_n)$ (the generalized Bergman) spaces, for $01$, $j=1,\dots,n$. Here $\vec \mu=(\mu_1,\dots,\mu_n)$ and each $\mu_j$ is a positive Borel measure on the interval $[0,1)$. Also we present a class of invariant spaces under the action of this operator.

#### Article information

Source
Taiwanese J. Math., Volume 7, Number 2 (2003), 293-308.

Dates
First available in Project Euclid: 20 July 2017

https://projecteuclid.org/euclid.twjm/1500575066

Digital Object Identifier
doi:10.11650/twjm/1500575066

Mathematical Reviews number (MathSciNet)
MR1978018

#### Citation

Chang, Der-Chen; Stevi ´c, Stevo. THE GENERALIZED CES`ARO OPERATOR ON THE UNIT POLYDISK. Taiwanese J. Math. 7 (2003), no. 2, 293--308. doi:10.11650/twjm/1500575066. https://projecteuclid.org/euclid.twjm/1500575066