### Abstract

Suppose that ƒ is in L^{2}(Δ) where Δ is the unit disk, and that ƒ = 0 outside Δ. We show that then the Cauchy transform Cƒ of ƒ, when restricted to Δ, satisfies ƖƖCfƖƖ_{2} ≤ (2/α)ƖƖƒƖƖ_{2}, where α ≈ 2.4048 is the smallest positive zero of the Bessel function Jo. This inequality is sharp.

Original language | English (US) |
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Pages (from-to) | 179-185 |

Number of pages | 7 |

Journal | Proceedings of the American Mathematical Society |

Volume | 107 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1989 |

Externally published | Yes |

### Keywords

- Link homotopy
- Links
- Whitney trick

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Anderson, J. M., & Hinkkanen, A. (1989). The cauchy transform on bounded domains.

*Proceedings of the American Mathematical Society*,*107*(1), 179-185. https://doi.org/10.1090/S0002-9939-1989-0972226-5