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http://dx.doi.org/10.4134/CKMS.c200418

TOEPLITZ AND HANKEL OPERATORS WITH CARLESON MEASURE SYMBOLS  

Park, Jaehui (Research Institute of Mathematics Seoul National University)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.1, 2022 , pp. 91-103 More about this Journal
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.
Keywords
Toeplitz operators; Hankel operators; densely defined operators; Carleson measures;
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