Taiwanese Journal of Mathematics

THE GENERALIZED CES`ARO OPERATOR ON THE UNIT POLYDISK

Der-Chen Chang and Stevo Stevi ´c

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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

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500575066

Digital Object Identifier
doi:10.11650/twjm/1500575066

Mathematical Reviews number (MathSciNet)
MR1978018

Subjects
Primary: 47B38: Operators on function spaces (general) 46E15: Banach spaces of continuous, differentiable or analytic functions

Keywords
analytic functions Ces\` aro operator polydisk Hardy spaces Bergman spaces invariant spaces

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


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