Authors: | Stević, Stevo Jiang, Zhi Jie |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Compactness of the differences of weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball | Journal: | Taiwanese Journal of Mathematics | Volume: | 15 | Issue: | 6 | First page: | 2647 | Last page: | 2665 | Issue Date: | 1-Jan-2011 | Rank: | M22 | ISSN: | 1027-5487 | DOI: | 10.11650/twjm/1500406489 | Abstract: | Let Φ1 and Φ2 be holomorphic self-maps of the open unit ball B in CN, u1 and u2 be holomorphic functions on B and let weighted composition operators W Φ1,u1; WΦ2,u2: Apα → H∞v be bounded. This paper characterizes the compactness of the difference of these operators from the weighted Bergman space Apα, 0 < p < ∞, α >-1, to the weighted-type space H∞v of holomorphic functions on B in terms of inducing symbols Φ1, Φ2, u1 and u2. For the case p > 1 we find an asymptotically equivalent expression to the essential norm of the operator. |
Keywords: | Compact operator | Essential norm | Weighted bergman space | Weighted composition operator | Weighted-type space | Publisher: | Mathematical Society of the Republic of China | Project: | Science Foundation of Sichuan Province (No.09ZC115) |
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