Szegö and Bergman projections on non-smooth planar domains

  • Loredana Lanzani
  • Elias M. Stein
Article

Abstract

We establish Lp 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 Lp 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.

Math Subject Classifications

30E20 30E25 31A10 30C20 30C40 30C45 

Key Words and Phrases

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

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Copyright information

© Mathematica Josephina, Inc. 2004

Authors and Affiliations

  • Loredana Lanzani
    • 1
    • 2
  • Elias M. Stein
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of ArkansasFayetteville
  2. 2.Department of MathematicsPrinceton UniversityPrinceton

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