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Volume 25, Issue 2
A Theorem of Nehari Type on the Bergman Space

Yufeng Lu & Jun Yang

Commun. Math. Res., 25 (2009), pp. 159-164.

Published online: 2021-06

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  • Abstract

In this paper we concern with the characterization of bounded linear operators $S$ acting on the weighted Bergman spaces on the unit ball. It is shown that, if $S$ satisfies the commutation relation $ST_{z_i} = T_{\overline{z}_i}S(i = 1, · · · , n)$, where $T_{z_i} = z_if$ and $T_{\overline{z}_i} = P(\overline{z}_if)$ where $P$ is the weighted Bergman projection, then $S$ must be a Hankel operator.

  • Keywords

Bergman space, unit ball, Hankel operator.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jyang@ysu.edu.cn (Jun Yang)

  • BibTex
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  • TXT
@Article{CMR-25-159, author = {Yufeng and Lu and and 18136 and and Yufeng Lu and Jun and Yang and jyang@ysu.edu.cn and 18137 and College of Science, Yanshan University, Qinhuangdao 066004, China and Jun Yang}, title = {A Theorem of Nehari Type on the Bergman Space}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {25}, number = {2}, pages = {159--164}, abstract = {

In this paper we concern with the characterization of bounded linear operators $S$ acting on the weighted Bergman spaces on the unit ball. It is shown that, if $S$ satisfies the commutation relation $ST_{z_i} = T_{\overline{z}_i}S(i = 1, · · · , n)$, where $T_{z_i} = z_if$ and $T_{\overline{z}_i} = P(\overline{z}_if)$ where $P$ is the weighted Bergman projection, then $S$ must be a Hankel operator.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19302.html} }
TY - JOUR T1 - A Theorem of Nehari Type on the Bergman Space AU - Lu , Yufeng AU - Yang , Jun JO - Communications in Mathematical Research VL - 2 SP - 159 EP - 164 PY - 2021 DA - 2021/06 SN - 25 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19302.html KW - Bergman space, unit ball, Hankel operator. AB -

In this paper we concern with the characterization of bounded linear operators $S$ acting on the weighted Bergman spaces on the unit ball. It is shown that, if $S$ satisfies the commutation relation $ST_{z_i} = T_{\overline{z}_i}S(i = 1, · · · , n)$, where $T_{z_i} = z_if$ and $T_{\overline{z}_i} = P(\overline{z}_if)$ where $P$ is the weighted Bergman projection, then $S$ must be a Hankel operator.

YufengLu & JunYang. (2021). A Theorem of Nehari Type on the Bergman Space. Communications in Mathematical Research . 25 (2). 159-164. doi:
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