### Abstract

The aim of this work is to provide a geometric characterization of the positive Radon measures µ with compact support on the plane such that the associated Cauchy transform defines a compact operator from L ^{2} (µ) to L ^{2} (µ). It turns out that a crucial role is played by the density of the measure and by its Menger curvature.

Original language | English (US) |
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Pages (from-to) | 2069-2080 |

Number of pages | 12 |

Journal | Proceedings of the American Mathematical Society |

Volume | 147 |

Issue number | 5 |

DOIs | |

State | Published - May 2019 |

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## Cite this

Puliatti, C., & Mayboroda, S. (2019). Measures that define a compact cauchy transform.

*Proceedings of the American Mathematical Society*,*147*(5), 2069-2080. https://doi.org/10.1090/proc/14419