### Abstract

Let Δ be an equilateral cone in C with vertices at the complex numbers 0, z_{1} ^{0}, z_{2} ^{0} and rigid base M (Section 1). Assume that the positive real semi-axis is the bisectrix of the angle at the origin. For the base M of the cone Δ we derive a Carleman formula representing all those holomorphic functions f ∈ H (Δ) from their boundary values (if they exist) on M which belong to the class NH_{M} ^{1} (Δ). The class NH_{M} ^{1} (Δ) is the class of holomorphic functions in Δ which belong to the Hardy class H^{1} near the base M (Section 2). As an application of the above characterization, an important result is an extension theorem for a function f ∈ L^{1} (M) to a function f ∈ NH_{M} ^{1} (Δ).

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

Pages (from-to) | 657-672 |

Number of pages | 16 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 310 |

Issue number | 2 |

DOIs | |

Publication status | Published - 15 Oct 2005 |

### Keywords

- Carleman formula
- Cone with a rigid base