## Abstract

Let sript U sign be a bounded, simply connected domain with Jordan rectifiable boundary and let M ⊂ ∂ sript U sign be an open analytic arc whose Lebesgue measure satisfies 0 < m(M) < m(∂ sript U sign. Our result gives a complete description of the class of holomorphic functions in sript U sign which are represented by the Carleman formulas on the open arc M, when ∂ sript U sign is almost regular with respect to M (Section 2). That is, we give a type of integral representation formulas for functions holomorphic in a domain sript U sign by its values on a part M of the boundary ∂ sript U sign. This class is denoted by sript N sign ℋ^{1} _{M}(sript U sign).

Original language | English |
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Pages (from-to) | 289-301 |

Number of pages | 13 |

Journal | Monatshefte fur Mathematik |

Volume | 149 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 2006 |

## Keywords

- Analytic curves
- Carleman formulas
- Smirnov classes