Logarithmic Bergman-type space and a sum of product-type operators

Yan-fu Xue; Zhi-jie jiang; Hui-ling Jin; Xiao-feng Peng; Yan-fu Xue; Zhi-jie jiang; Hui-ling Jin; Xiao-feng Peng

doi:10.3934/math.20231365

AIMS Mathematics

2023, Volume 8, Issue 11: 26682-26702. doi: 10.3934/math.20231365

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Logarithmic Bergman-type space and a sum of product-type operators

1.
School of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, China
2.
South Sichuan Center for Applied Mathematics, Sichuan University of Science and Engineering, Zigong, Sichuan, 643000, China

Received: 09 July 2023 Revised: 30 August 2023 Accepted: 03 September 2023 Published: 19 September 2023
MSC : 47B38, 47B33, 47B37, 30H05

One of the aims of the present paper is to obtain some properties about logarithmic Bergman-type space on the unit ball. As some applications, the bounded and compact operators $ \mathfrak{S}^m_{\vec{u}, {\varphi}} = \sum_{i = 0}^{m}M_{u_i}C_{\varphi}\Re^{i} $ from logarithmic Bergman-type space to weighted-type space on the unit ball are completely characterized.
- product-type operator,
- boundedness,
- compactness,
- logarithmic Bergman-type space,
- weighted-type space
Citation: Yan-fu Xue, Zhi-jie jiang, Hui-ling Jin, Xiao-feng Peng. Logarithmic Bergman-type space and a sum of product-type operators[J]. AIMS Mathematics, 2023, 8(11): 26682-26702. doi: 10.3934/math.20231365

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Abstract

One of the aims of the present paper is to obtain some properties about logarithmic Bergman-type space on the unit ball. As some applications, the bounded and compact operators $ \mathfrak{S}^m_{\vec{u}, {\varphi}} = \sum_{i = 0}^{m}M_{u_i}C_{\varphi}\Re^{i} $ from logarithmic Bergman-type space to weighted-type space on the unit ball are completely characterized.

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