### Abstract

We study bounded holomorphic functions n on the unit ball B_{n}of C satisfying the following so-called Cauchy integral equalities:for some sequence λ_{m}depending on π. Among the applications are the Ahern-Rudin problem concerning the composition property of holomorphic functions on B_{n}, a projection theorem about the orthogonal projection of H^{2}(B_{n}) onto the closed subspace generated by holomorphic polynomials in π, and some new information about the inner functions. In particular, it is shown that if we interpret BMOA(B_{n}) as the dual of H^{1}(B_{n}), then the map g → g o π is a linear isometry of BMOA(B_{1}) into BMOA(B_{n}) for every inner function π on B_{n}such that π(0) = 0.

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

Pages (from-to) | 337-352 |

Number of pages | 16 |

Journal | Transactions of the American Mathematical Society |

Volume | 315 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1989 |

Externally published | Yes |

### Fingerprint

### Keywords

- Cauchy Integral Equalities
- Projection
- The Ahern-Rudin problem

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**Cauchy integral equalities and applications.** / Choe, Boo Rim.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 315, no. 1, pp. 337-352. https://doi.org/10.1090/S0002-9947-1989-0935531-9

}

TY - JOUR

T1 - Cauchy integral equalities and applications

AU - Choe, Boo Rim

PY - 1989

Y1 - 1989

N2 - We study bounded holomorphic functions n on the unit ball Bnof C satisfying the following so-called Cauchy integral equalities:for some sequence λmdepending on π. Among the applications are the Ahern-Rudin problem concerning the composition property of holomorphic functions on Bn, a projection theorem about the orthogonal projection of H2(Bn) onto the closed subspace generated by holomorphic polynomials in π, and some new information about the inner functions. In particular, it is shown that if we interpret BMOA(Bn) as the dual of H1(Bn), then the map g → g o π is a linear isometry of BMOA(B1) into BMOA(Bn) for every inner function π on Bnsuch that π(0) = 0.

AB - We study bounded holomorphic functions n on the unit ball Bnof C satisfying the following so-called Cauchy integral equalities:for some sequence λmdepending on π. Among the applications are the Ahern-Rudin problem concerning the composition property of holomorphic functions on Bn, a projection theorem about the orthogonal projection of H2(Bn) onto the closed subspace generated by holomorphic polynomials in π, and some new information about the inner functions. In particular, it is shown that if we interpret BMOA(Bn) as the dual of H1(Bn), then the map g → g o π is a linear isometry of BMOA(B1) into BMOA(Bn) for every inner function π on Bnsuch that π(0) = 0.

KW - Cauchy Integral Equalities

KW - Projection

KW - The Ahern-Rudin problem

UR - http://www.scopus.com/inward/record.url?scp=0012472523&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0012472523&partnerID=8YFLogxK

U2 - 10.1090/S0002-9947-1989-0935531-9

DO - 10.1090/S0002-9947-1989-0935531-9

M3 - Article

AN - SCOPUS:0012472523

VL - 315

SP - 337

EP - 352

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 1

ER -