Szegö and Bergman projections on non-smooth planar domains

Loredana Lanzani, Elias M. Stein

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

We establish L p regularity for the Szegö and Bergman projections associated to a simply connected planar domain in any of the following classes: vanishing chord arc; Lipschitz; Ahlfors-regular; or local graph (for the Szegö projection to be well defined, the local graph curve must be rectifiable). As applications, we obtain L p regularity for the Riesz transforms, as well as Sobolev space regularity for the non-homogeneous Dirichlet problem associated to any of the domains above and, more generally, to an arbitrary proper simply connected domain in the plane.

Original languageEnglish (US)
Pages (from-to)63-86
Number of pages24
JournalJournal of Geometric Analysis
Volume14
Issue number1
DOIs
StatePublished - Dec 1 2004
Externally publishedYes

Keywords

  • Ahlfors-regular curve
  • Bergman projection
  • Dirichlet problem
  • Lipschitz curve
  • Riesz transform
  • Szegö projection
  • chord arc curve
  • conformal map

ASJC Scopus subject areas

  • Geometry and Topology

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