Szego projection versus potential theory for non-smooth planar domains

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
Pages (from-to)537-555
Number of pages19
JournalIndiana University Mathematics Journal
Volume48
Issue number2
StatePublished - Jun 1999
Externally publishedYes

Fingerprint

Potential Theory
Lipschitz
Stein Equation
Projection
Argand diagram
Dirichlet Problem
Bounded Domain
Operator
Theorem

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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

In: Indiana University Mathematics Journal, Vol. 48, No. 2, 06.1999, p. 537-555.

Research output: Contribution to journalArticle

@article{2c5d79368fa24978b2470d8cc1ad8bf3,
title = "Szego projection versus potential theory for non-smooth planar domains",
abstract = "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.",
author = "Loredana Lanzani",
year = "1999",
month = "6",
language = "English (US)",
volume = "48",
pages = "537--555",
journal = "Indiana University Mathematics Journal",
issn = "0022-2518",
publisher = "Indiana University",
number = "2",

}

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 -