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Toeplitz and Hankel operators with Carleson measure symbols

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대한수학회 (The Korean Mathematical Society)|2022.01|대한수학회논문집 (Communications of the KMS)|제37권 제1호|pp. 91-103|DOI 10.4134/CKMS.c200418

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키워드

Toeplitz operatorsHankel operatorsdensely defined operatorsCarleson measures
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초록

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.

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.

참고문헌 (26)

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