Revisit to a theorem of Wogen

Hyungwoon Koo; Maofa Wang

doi:10.1007/978-3-0346-0158-0_20

Revisit to a theorem of Wogen

Hyungwoon Koo, Maofa Wang

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Citations (Scopus)

Abstract

In this note we provide a new proof of a theorem of Wogen on the boundedness criterion for composition operators on Hardy space H²(Uⁿ) induced by holomorphic self-maps of the unit ball Uⁿ, and then generalize it to more general inducing self-maps.

Original language	English
Title of host publication	Topics in Operator Theory
Subtitle of host publication	Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008
Editors	Joseph A. Ball, Vladimir Bolotnikov, Leiba Rodman, Ilya M. Spitkovsky, J. William Helton
Publisher	Springer International Publishing
Pages	355-363
Number of pages	9
ISBN (Print)	9783034601573
DOIs	https://doi.org/10.1007/978-3-0346-0158-0_20
Publication status	Published - 2010
Event	19th International Workshop on Operator Theory and its Applications, IWOTA 2008 - Williamsburg, United States Duration: 2008 Jul 22 → 2008 Jul 26

Publication series

Name	Operator Theory: Advances and Applications
Volume	202
ISSN (Print)	0255-0156
ISSN (Electronic)	2296-4878

Other

Other	19th International Workshop on Operator Theory and its Applications, IWOTA 2008
Country/Territory	United States
City	Williamsburg
Period	08/7/22 → 08/7/26

Keywords

Bergman space
Boundedness
Carleson measure
Composition operator
Hardy space
Smooth map
Wogen criterion

ASJC Scopus subject areas

Analysis

Access to Document

10.1007/978-3-0346-0158-0_20

Cite this

Koo, H., & Wang, M. (2010). Revisit to a theorem of Wogen. In J. A. Ball, V. Bolotnikov, L. Rodman, I. M. Spitkovsky, & J. W. Helton (Eds.), Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008 (pp. 355-363). (Operator Theory: Advances and Applications; Vol. 202). Springer International Publishing. https://doi.org/10.1007/978-3-0346-0158-0_20

Revisit to a theorem of Wogen. / Koo, Hyungwoon; Wang, Maofa.

Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008. ed. / Joseph A. Ball; Vladimir Bolotnikov; Leiba Rodman; Ilya M. Spitkovsky; J. William Helton. Springer International Publishing, 2010. p. 355-363 (Operator Theory: Advances and Applications; Vol. 202).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Koo, H & Wang, M 2010, Revisit to a theorem of Wogen. in JA Ball, V Bolotnikov, L Rodman, IM Spitkovsky & JW Helton (eds), Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008. Operator Theory: Advances and Applications, vol. 202, Springer International Publishing, pp. 355-363, 19th International Workshop on Operator Theory and its Applications, IWOTA 2008, Williamsburg, United States, 08/7/22. https://doi.org/10.1007/978-3-0346-0158-0_20

Koo H, Wang M. Revisit to a theorem of Wogen. In Ball JA, Bolotnikov V, Rodman L, Spitkovsky IM, Helton JW, editors, Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008. Springer International Publishing. 2010. p. 355-363. (Operator Theory: Advances and Applications). doi: 10.1007/978-3-0346-0158-0_20

Koo, Hyungwoon ; Wang, Maofa. / Revisit to a theorem of Wogen. Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008. editor / Joseph A. Ball ; Vladimir Bolotnikov ; Leiba Rodman ; Ilya M. Spitkovsky ; J. William Helton. Springer International Publishing, 2010. pp. 355-363 (Operator Theory: Advances and Applications).

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abstract = "In this note we provide a new proof of a theorem of Wogen on the boundedness criterion for composition operators on Hardy space H2(Un) induced by holomorphic self-maps of the unit ball Un, and then generalize it to more general inducing self-maps.",

keywords = "Bergman space, Boundedness, Carleson measure, Composition operator, Hardy space, Smooth map, Wogen criterion",

author = "Hyungwoon Koo and Maofa Wang",

note = "Publisher Copyright: {\textcopyright} 2010 Birkh{\"a}user Verlag Basel/Switzerland.; 19th International Workshop on Operator Theory and its Applications, IWOTA 2008 ; Conference date: 22-07-2008 Through 26-07-2008",

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AB - In this note we provide a new proof of a theorem of Wogen on the boundedness criterion for composition operators on Hardy space H2(Un) induced by holomorphic self-maps of the unit ball Un, and then generalize it to more general inducing self-maps.

KW - Bergman space

KW - Boundedness

KW - Carleson measure

KW - Composition operator

KW - Hardy space

KW - Smooth map

KW - Wogen criterion

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BT - Topics in Operator Theory

A2 - Ball, Joseph A.

A2 - Bolotnikov, Vladimir

A2 - Rodman, Leiba

A2 - Spitkovsky, Ilya M.

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PB - Springer International Publishing

T2 - 19th International Workshop on Operator Theory and its Applications, IWOTA 2008

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ER -

Revisit to a theorem of Wogen

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