### Abstract

We show that the Kerzman-Stein operator associated to a bounded planar domain Ω with C^{1}-boundary is compact in L^{2}(bΩ). We establish the Kerzman-Stein equation for the Szego projection associated to a bounded planar domain with Lipschitz boundary. As an application, we extend to the Lipschitz setting a theorem of S. Bell for representing the solution of the classical Dirichlet problem on a simply connected bounded domain in the complex plane.

Original language | English (US) |
---|---|

Pages (from-to) | 537-555 |

Number of pages | 19 |

Journal | Indiana University Mathematics Journal |

Volume | 48 |

Issue number | 2 |

State | Published - Jun 1999 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Szego projection versus potential theory for non-smooth planar domains.** / Lanzani, Loredana.

Research output: Contribution to journal › Article

*Indiana University Mathematics Journal*, vol. 48, no. 2, pp. 537-555.

}

TY - JOUR

T1 - Szego projection versus potential theory for non-smooth planar domains

AU - Lanzani, Loredana

PY - 1999/6

Y1 - 1999/6

N2 - We show that the Kerzman-Stein operator associated to a bounded planar domain Ω with C1-boundary is compact in L2(bΩ). We establish the Kerzman-Stein equation for the Szego projection associated to a bounded planar domain with Lipschitz boundary. As an application, we extend to the Lipschitz setting a theorem of S. Bell for representing the solution of the classical Dirichlet problem on a simply connected bounded domain in the complex plane.

AB - We show that the Kerzman-Stein operator associated to a bounded planar domain Ω with C1-boundary is compact in L2(bΩ). We establish the Kerzman-Stein equation for the Szego projection associated to a bounded planar domain with Lipschitz boundary. As an application, we extend to the Lipschitz setting a theorem of S. Bell for representing the solution of the classical Dirichlet problem on a simply connected bounded domain in the complex plane.

UR - http://www.scopus.com/inward/record.url?scp=0040714402&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040714402&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0040714402

VL - 48

SP - 537

EP - 555

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 2

ER -