### 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 |
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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 Sep |

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics