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2003 THE GENERALIZED CES`ARO OPERATOR ON THE UNIT POLYDISK
Der-Chen Chang, Stevo Stevi ´c
Taiwanese J. Math. 7(2): 293-308 (2003). DOI: 10.11650/twjm/1500575066

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.

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Der-Chen Chang. Stevo Stevi ´c. "THE GENERALIZED CES`ARO OPERATOR ON THE UNIT POLYDISK." Taiwanese J. Math. 7 (2) 293 - 308, 2003. https://doi.org/10.11650/twjm/1500575066

Information

Published: 2003
First available in Project Euclid: 20 July 2017

MathSciNet: MR1978018
Digital Object Identifier: 10.11650/twjm/1500575066

Subjects:
Primary: ‎46E15, 47B38

Rights: Copyright © 2003 The Mathematical Society of the Republic of China

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