### 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 |

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 | |

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) | 0255-0156 |

ISSN (Electronic) | 2296-4878 |

### 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 |

### Keywords

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

### ASJC Scopus subject areas

- Analysis

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## 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