Toeplitz and Hankel operators with Carleson measure symbols
Commun. Korean Math. Soc. 2022 Vol. 37, No. 1, 91-103
https://doi.org/10.4134/CKMS.c200418
Published online May 17, 2021
Printed January 31, 2022
Jaehui Park
Seoul National University
Abstract : In this paper, we introduce Toeplitz operators and Hankel operators with complex Borel measures on the closed unit disk. When a positive measure $\mu$ 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 $\mu$ on $\mathbb{D}$, $\mu$ is a Carleson measure if and only if the Toeplitz operator with symbol $\mu$ 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
MSC numbers : Primary 47B35, 47L60, 28A25
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