Hankel operators in the Bergman space and schatten p-classes: The case K p < 2

Jingbo Xia

doi:10.1090/s0002-9939-01-06217-7

Hankel operators in the Bergman space and schatten p-classes: The case K p < 2

Jingbo Xia

Mathematics

University at Buffalo

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

K. Zhu proved in Amer. J. Math. 113 (1991), 147-167, that, for 2 < p < co, the Hankel operators H_f and H_f on the Bergman space belong to the Schatten class C_p if and only if the mean oscillation MO(f)(z) = {|/|²) - f/(2)|²}^1/2 belongs to £"(£,(| - \z\²)-²dA(z)). In this paper we prove that the same result also holds when 1 < p < 2.

Original language	English
Pages (from-to)	3559-3567
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	129
Issue number	12
DOIs	https://doi.org/10.1090/s0002-9939-01-06217-7
State	Published - 2001

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title = "Hankel operators in the Bergman space and schatten p-classes: The case K p < 2",

abstract = "K. Zhu proved in Amer. J. Math. 113 (1991), 147-167, that, for 2 < p < co, the Hankel operators Hf and Hf on the Bergman space belong to the Schatten class Cp if and only if the mean oscillation MO(f)(z) = \{|/|2) - f/(2)|2\}1/2 belongs to £{"}(£,(| - \textbackslash{}z\textbackslash{}2)-2dA(z)). In this paper we prove that the same result also holds when 1 < p < 2.",

author = "Jingbo Xia",

year = "2001",

doi = "10.1090/s0002-9939-01-06217-7",

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T1 - Hankel operators in the Bergman space and schatten p-classes

T2 - The case K p < 2

AU - Xia, Jingbo

PY - 2001

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N2 - K. Zhu proved in Amer. J. Math. 113 (1991), 147-167, that, for 2 < p < co, the Hankel operators Hf and Hf on the Bergman space belong to the Schatten class Cp if and only if the mean oscillation MO(f)(z) = {|/|2) - f/(2)|2}1/2 belongs to £"(£,(| - \z\2)-2dA(z)). In this paper we prove that the same result also holds when 1 < p < 2.

AB - K. Zhu proved in Amer. J. Math. 113 (1991), 147-167, that, for 2 < p < co, the Hankel operators Hf and Hf on the Bergman space belong to the Schatten class Cp if and only if the mean oscillation MO(f)(z) = {|/|2) - f/(2)|2}1/2 belongs to £"(£,(| - \z\2)-2dA(z)). In this paper we prove that the same result also holds when 1 < p < 2.

UR - https://www.scopus.com/pages/publications/23044530521

U2 - 10.1090/s0002-9939-01-06217-7

DO - 10.1090/s0002-9939-01-06217-7

M3 - Article

SN - 0002-9939

VL - 129

SP - 3559

EP - 3567

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 12

ER -

Hankel operators in the Bergman space and schatten p-classes: The case K p < 2

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