Banach Journal of Mathematical Analysis

On some properties of a differential operator on the polydisk

Songxiao Li and Romi Shamoyan

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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

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

First available in Project Euclid: 21 April 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

differentiation operator weighted Bergman space Hardy space polydisk


Shamoyan, Romi; Li, Songxiao. On some properties of a differential operator on the polydisk. Banach J. Math. Anal. 3 (2009), no. 1, 68--84. doi:10.15352/bjma/1240336425.

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