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Title: Infinite-dimensional hilbert tensors on spaces of analytic functions
Authors: Song, Y
Qi, L 
Keywords: Analytic function
Bergman space
Gamma function
Hilbert tensor
Upper bound
Issue Date: 2017
Publisher: International Press
Source: Communications in mathematical sciences, 2017, v. 15, no. 7, p. 1897-1911 How to cite?
Journal: Communications in mathematical sciences 
Abstract: In this paper, the mth order infinite dimensional Hilbert tensor (hypermatrix) is introduced to define an (m-1)-homogeneous operator on the spaces of analytic functions, which is called the Hilbert tensor operator. The boundedness of the Hilbert tensor operator is presented on Bergman spaces Ap (p &gtMergeCell 2(m-1)). On the base of the boundedness, two positively homogeneous operators are introduced to the spaces of analytic functions, and hence the upper bounds of norm of the two operators are found on Bergman spaces Ap (p &gtMergeCell 2(m-1)). In particular, the norms of such two operators on Bergman spaces A4(m-1) are smaller than or equal to π and π1/m-1, respectively.
ISSN: 1539-6746
EISSN: 1945-0796
DOI: 10.4310/CMS.2017.v15.n7.a5
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