Journal of the Mathematical Society of Japan

Reducing subspaces of multiplication operators on weighted Hardy spaces over bidisk

Shuhei KUWAHARA

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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 $M_{zw}$.

Article information

Source
J. Math. Soc. Japan, Volume 69, Number 4 (2017), 1555-1563.

Dates
First available in Project Euclid: 25 October 2017

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1508918568

Digital Object Identifier
doi:10.2969/jmsj/06941555

Mathematical Reviews number (MathSciNet)
MR3715815

Zentralblatt MATH identifier
06821651

Subjects
Primary: 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Secondary: 30H20: Bergman spaces, Fock spaces

Keywords
reducing subspaces weighted Hardy spaces over bidisk

Citation

KUWAHARA, Shuhei. Reducing subspaces of multiplication operators on weighted Hardy spaces over bidisk. J. Math. Soc. Japan 69 (2017), no. 4, 1555--1563. doi:10.2969/jmsj/06941555. https://projecteuclid.org/euclid.jmsj/1508918568


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