Volume 26, Issue 4
Little Hankel Operators on the Weighted Bergman Space of the Unit Ball

Commun. Math. Res., 26 (2010), pp. 304-312.

Published online: 2021-05

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• Abstract

In this paper we mainly consider little Hankel operators with square-integrable symbols on the weighted Bergman spaces of the unit ball. We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that $SMO(f) ∈ L^{\frac{p}{2}}(B_n, dλ)$ and $2 ≤ p < ∞,$ which is very important to research the relation between Toeplitz operators and little Hankel operators.

• Keywords

weighted Bergman space, little Hankel operator, unit ball.

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@Article{CMR-26-304, author = {Zhang , KanLu , Yufeng and Liu , Chaomei}, title = {Little Hankel Operators on the Weighted Bergman Space of the Unit Ball}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {26}, number = {4}, pages = {304--312}, abstract = {

In this paper we mainly consider little Hankel operators with square-integrable symbols on the weighted Bergman spaces of the unit ball. We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that $SMO(f) ∈ L^{\frac{p}{2}}(B_n, dλ)$ and $2 ≤ p < ∞,$ which is very important to research the relation between Toeplitz operators and little Hankel operators.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19133.html} }
TY - JOUR T1 - Little Hankel Operators on the Weighted Bergman Space of the Unit Ball AU - Zhang , Kan AU - Lu , Yufeng AU - Liu , Chaomei JO - Communications in Mathematical Research VL - 4 SP - 304 EP - 312 PY - 2021 DA - 2021/05 SN - 26 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19133.html KW - weighted Bergman space, little Hankel operator, unit ball. AB -

In this paper we mainly consider little Hankel operators with square-integrable symbols on the weighted Bergman spaces of the unit ball. We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that $SMO(f) ∈ L^{\frac{p}{2}}(B_n, dλ)$ and $2 ≤ p < ∞,$ which is very important to research the relation between Toeplitz operators and little Hankel operators.

KanZhang, YufengLu & ChaomeiLiu. (2021). Little Hankel Operators on the Weighted Bergman Space of the Unit Ball. Communications in Mathematical Research . 26 (4). 304-312. doi:
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