Essential norm of a product-type operator from Bergman space to weighted-type space

Volume 10, Issue 8, pp 4269--4274 http://dx.doi.org/10.22436/jnsa.010.08.21

Publication Date: August 20, 2017 Submission Date: July 10, 2017

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Authors

Ya-Song Chen - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, P. R. China. Zhong-Shan Fang - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, P. R. China. Yeong-Cheng Liou - Department of Healthcare Administration and Medical Informatics, Center for Big Data Analytics and Intelligent Healthcare, and Research Center of Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, Taiwan. - Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 807, Taiwan.

Abstract

In this paper, we discuss the boundedness of a product-type operator introduced by Stević, which acting from Bergman space to the weighted-type spaces or the little weighted-type spaces in the unit ball, and characterize the the essential norm of the product-type operator. From which the sufficient and necessary condition of compactness of this type operator follows immediately.

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Keywords

• Product-type operator
• Bergman space
• weighted-type space
• unit ball.

MSC

•  47B38
•  47B33
•  45P0

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