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October, 2017 Reducing subspaces of multiplication operators on weighted Hardy spaces over bidisk
Shuhei KUWAHARA
J. Math. Soc. Japan 69(4): 1555-1563 (October, 2017). DOI: 10.2969/jmsj/06941555

Abstract

We consider weighted Hardy spaces over bidisk ${\mathbb D}^2$ which generalize the weighted Bergman spaces $A_\alpha^2({\mathbb D}^2)$. Let $z,w$ be coordinate functions and $M_{z^Nw^N}$ the multiplication by $z^Nw^N$ for a natural number $N$. In this paper, we study the reducing subspaces of $M_{z^Nw^N}$. In particular, we obtain the minimal reducing subspaces of $M_{zw}$.

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Shuhei KUWAHARA. "Reducing subspaces of multiplication operators on weighted Hardy spaces over bidisk." J. Math. Soc. Japan 69 (4) 1555 - 1563, October, 2017. https://doi.org/10.2969/jmsj/06941555

Information

Published: October, 2017
First available in Project Euclid: 25 October 2017

zbMATH: 06821651
MathSciNet: MR3715815
Digital Object Identifier: 10.2969/jmsj/06941555

Subjects:
Primary: 47B37
Secondary: 30H20

Keywords: reducing subspaces , weighted Hardy spaces over bidisk

Rights: Copyright © 2017 Mathematical Society of Japan

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Vol.69 • No. 4 • October, 2017
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