### Abstract

For a given holomorphic self map p of the unit disk, we consider the Bloch-to-BMOA composition property (pullback property) of Our results are (1) cannot have the pullback property if touches the boundary too smoothly, (2) while has the pullback property if touches the boundary rather sharply. One of these results yields an interesting consequence completely contrary to a higher dimensional result which has been known. These results resemble known results concerning the compactness of composition operators on the Hardy spaces. Some remarks in that direction are included.

Original language | English |
---|---|

Pages (from-to) | 2987-2996 |

Number of pages | 10 |

Journal | Proceedings of the American Mathematical Society |

Volume | 125 |

Issue number | 10 |

Publication status | Published - 1997 Dec 1 |

### Fingerprint

### Keywords

- Bloch space
- BMOA
- Pullback property

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Proceedings of the American Mathematical Society*,

*125*(10), 2987-2996.

**Bloch-to-BMOA pullbacks on the disk.** / Choe, Boo Rim; Ramey, Wade; Ullrich, David.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 125, no. 10, pp. 2987-2996.

}

TY - JOUR

T1 - Bloch-to-BMOA pullbacks on the disk

AU - Choe, Boo Rim

AU - Ramey, Wade

AU - Ullrich, David

PY - 1997/12/1

Y1 - 1997/12/1

N2 - For a given holomorphic self map p of the unit disk, we consider the Bloch-to-BMOA composition property (pullback property) of Our results are (1) cannot have the pullback property if touches the boundary too smoothly, (2) while has the pullback property if touches the boundary rather sharply. One of these results yields an interesting consequence completely contrary to a higher dimensional result which has been known. These results resemble known results concerning the compactness of composition operators on the Hardy spaces. Some remarks in that direction are included.

AB - For a given holomorphic self map p of the unit disk, we consider the Bloch-to-BMOA composition property (pullback property) of Our results are (1) cannot have the pullback property if touches the boundary too smoothly, (2) while has the pullback property if touches the boundary rather sharply. One of these results yields an interesting consequence completely contrary to a higher dimensional result which has been known. These results resemble known results concerning the compactness of composition operators on the Hardy spaces. Some remarks in that direction are included.

KW - Bloch space

KW - BMOA

KW - Pullback property

UR - http://www.scopus.com/inward/record.url?scp=0040347157&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040347157&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0040347157

VL - 125

SP - 2987

EP - 2996

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 10

ER -