Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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TOEPLITZ AND HANKEL OPERATORS WITH CARLESON MEASURE SYMBOLS

  • Park, Jaehui (Research Institute of Mathematics Seoul National University)
  • Received : 2020.11.05
  • Accepted : 2021.02.03
  • Published : 2022.01.31
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Abstract

In this paper, we introduce Toeplitz operators and Hankel operators with complex Borel measures on the closed unit disk. When a positive measure 𝜇 on (-1, 1) is a Carleson measure, it is known that the corresponding Hankel matrix is bounded and vice versa. We show that for a positive measure 𝜇 on 𝔻, 𝜇 is a Carleson measure if and only if the Toeplitz operator with symbol 𝜇 is a densely defined bounded linear operator. We also study Hankel operators of Hilbert-Schmidt class.

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References

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