Banach Journal of Mathematical Analysis

On some properties of a differential operator on the polydisk

Songxiao Li and Romi Shamoyan

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Abstract

We study the action and properties of a differential operator in the polydisk, extending some classical results from the unit disk. Using so called dyadic decomposition of the polydisk we find precise connections between quazinorms of holomorphic function in the polydisk with quazinorms on the subframe and the unit disk. All our results were previously well-known in the unit disk.

Article information

Source
Banach J. Math. Anal. Volume 3, Number 1 (2009), 68-84.

Dates
First available: 21 April 2009

Permanent link to this document
http://projecteuclid.org/euclid.bjma/1240336425

Mathematical Reviews number (MathSciNet)
MR2461748

Zentralblatt MATH identifier
05379951

Digital Object Identifier
doi:10.15352/bjma/1240336425

Subjects
Primary: 32A18: Bloch functions, normal functions
Secondary: 32A36: Bergman spaces

Keywords
differentiation operator weighted Bergman space Hardy space polydisk

Citation

Shamoyan, Romi; Li, Songxiao. On some properties of a differential operator on the polydisk. Banach Journal of Mathematical Analysis 3 (2009), no. 1, 68--84. doi:10.15352/bjma/1240336425. http://projecteuclid.org/euclid.bjma/1240336425.


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