### Abstract

In this note we provide a new proof of a theorem of Wogen on the boundedness criterion for composition operators on Hardy space H^{2}(U^{n}) induced by holomorphic self-maps of the unit ball U^{n}, and then generalize it to more general inducing self-maps.

Original language | English |
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Title of host publication | Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008 |

Publisher | Springer International Publishing |

Pages | 355-363 |

Number of pages | 9 |

Volume | 202 |

ISBN (Print) | 9783034601573 |

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 |
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Volume | 202 |

ISSN (Print) | 02550156 |

ISSN (Electronic) | 22964878 |

### Other

Other | 19th International Workshop on Operator Theory and its Applications, IWOTA 2008 |
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Country | United States |

City | Williamsburg |

Period | 08/7/22 → 08/7/26 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Analysis

### Cite this

*Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008*(Vol. 202, pp. 355-363). (Operator Theory: Advances and Applications; Vol. 202). Springer International Publishing.

**Revisit to a theorem of Wogen.** / Koo, Hyung Woon; Wang, Maofa.

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

*Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008.*vol. 202, 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.

}

TY - GEN

T1 - Revisit to a theorem of Wogen

AU - Koo, Hyung Woon

AU - Wang, Maofa

PY - 2010

Y1 - 2010

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84975784155&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84975784155&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84975784155

SN - 9783034601573

VL - 202

T3 - Operator Theory: Advances and Applications

SP - 355

EP - 363

BT - Topics in Operator Theory: Volume 1: Operators, Matrices and Analytic Functions - Proceedings of the 19th International Workshop on Operator Theory and its Applications, 2008

PB - Springer International Publishing

ER -