Integrability of Mean Oscillation with Applications to Hankel Operators

Xiaofen Lv; Kehe Zhu

doi:10.1007/s00020-019-2504-8

Integrability of Mean Oscillation with Applications to Hankel Operators

Xiaofen Lv
, Kehe Zhu

Mathematics and Statistics

University at Albany

Huzhou University

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

6 Scopus citations

Abstract

We introduce and study a family of Banach spaces IMOps,σ of functions on the open unit ball B_n in Cⁿ, defined by an integrability condition of the mean oscillation in the Bergman metric. Our main results include a decomposition theorem for IMOps,σ, a characterization of holomorphic functions in IMOps,σ, and an application of IMOps,σ to the boundedness and compactness of Hankel operators between weighted Bergman spaces.

Original language	English
Article number	5
Journal	Integral Equations and Operator Theory
Volume	91
Issue number	1
DOIs	https://doi.org/10.1007/s00020-019-2504-8
State	Published - Feb 1 2019

Keywords

Bergman spaces
Hankel operators
Mean oscillation

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10.1007/s00020-019-2504-8

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title = "Integrability of Mean Oscillation with Applications to Hankel Operators",

abstract = "We introduce and study a family of Banach spaces IMOps,σ of functions on the open unit ball Bn in Cn, defined by an integrability condition of the mean oscillation in the Bergman metric. Our main results include a decomposition theorem for IMOps,σ, a characterization of holomorphic functions in IMOps,σ, and an application of IMOps,σ to the boundedness and compactness of Hankel operators between weighted Bergman spaces.",

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AU - Zhu, Kehe

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Y1 - 2019/2/1

N2 - We introduce and study a family of Banach spaces IMOps,σ of functions on the open unit ball Bn in Cn, defined by an integrability condition of the mean oscillation in the Bergman metric. Our main results include a decomposition theorem for IMOps,σ, a characterization of holomorphic functions in IMOps,σ, and an application of IMOps,σ to the boundedness and compactness of Hankel operators between weighted Bergman spaces.

AB - We introduce and study a family of Banach spaces IMOps,σ of functions on the open unit ball Bn in Cn, defined by an integrability condition of the mean oscillation in the Bergman metric. Our main results include a decomposition theorem for IMOps,σ, a characterization of holomorphic functions in IMOps,σ, and an application of IMOps,σ to the boundedness and compactness of Hankel operators between weighted Bergman spaces.

KW - Bergman spaces

KW - Hankel operators

KW - Mean oscillation

UR - https://www.scopus.com/pages/publications/85060904901

U2 - 10.1007/s00020-019-2504-8

DO - 10.1007/s00020-019-2504-8

M3 - Article

SN - 0378-620X

VL - 91

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 1

M1 - 5

ER -

Integrability of Mean Oscillation with Applications to Hankel Operators

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Keywords

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