Infinite-dimensional hilbert tensors on spaces of analytic functions

Yisheng Song, Liqun Qi

Research output: Journal article publicationJournal articleAcademic researchpeer-review

2 Citations (Scopus)


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 > 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 > 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.
Original languageEnglish
Pages (from-to)1897-1911
Number of pages15
JournalCommunications in Mathematical Sciences
Issue number7
Publication statusPublished - 1 Jan 2017


  • Analytic function
  • Bergman space
  • Gamma function
  • Hilbert tensor
  • Upper bound

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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