A+ CATEGORY SCIENTIFIC UNIT

Helson operators and coinvariant subspaces

Xiangdi Fu, Kunyu Guo, Fugang Yan Studia Mathematica MSC: Primary 47A15; Secondary 47B35, 30H20. DOI: 10.4064/sm220407-19-9 Published online: 26 October 2022

Abstract

We give an explicit expression of the functions in the finite-dimensional coinvariant subspace of the Hardy and weighted Bergman spaces over the infinite polydisc. As an application, an alternative form of the Perfekt–Pushnitski theorem characterizing Helson operators with finite rank is obtained. Interestingly, it turns out that a Helson operator is automatically bounded if it is of finite rank.

Authors

  • Xiangdi FuSchool of Mathematical Sciences
    Fudan University
    Shanghai, 200433, China
    e-mail
  • Kunyu GuoSchool of Mathematical Sciences
    Fudan University
    Shanghai, 200433, China
    e-mail
  • Fugang YanSchool of Mathematical Sciences
    Fudan University
    Shanghai, 200433, China
    e-mail

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