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Banach Journal of Mathematical Analysis

On some properties of a differential operator on the polydisk

Romi Shamoyan and Songxiao Li

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

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.

Primary Subjects: 32A18
Secondary Subjects: 32A36
Keywords: differentiation operator; weighted Bergman space; Hardy space; polydisk

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.bjma/1240336425
Mathematical Reviews number (MathSciNet): MR2461748
Zentralblatt MATH identifier: 05379951

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