Szegö and Bergman projections on non-smooth planar domains

Loredana Lanzani, Elias M. Stein

Research output: Contribution to journalArticle

32 Citations (Scopus)

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 - 2004
Externally publishedYes

Fingerprint

Bergman Projection
Regularity
Riesz Transform
Graph in graph theory
Chord or secant line
Sobolev Spaces
Dirichlet Problem
Lipschitz
Well-defined
Arc of a curve
Projection
Curve
Arbitrary

Keywords

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

ASJC Scopus subject areas

  • Geometry and Topology

Cite this

Szegö and Bergman projections on non-smooth planar domains. / Lanzani, Loredana; Stein, Elias M.

In: Journal of Geometric Analysis, Vol. 14, No. 1, 2004, p. 63-86.

Research output: Contribution to journalArticle

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