Hardy Spaces, Singular Integrals and The Geometry of Euclidean Domains of Locally Finite Perimeter

  • Steve Hofmann
  • Emilio Marmolejo-Olea
  • Marius Mitrea
  • Salvador Pérez-Esteva
  • Michael Taylor
Article

DOI: 10.1007/s00039-009-0015-5

Cite this article as:
Hofmann, S., Marmolejo-Olea, E., Mitrea, M. et al. Geom. Funct. Anal. (2009) 19: 842. doi:10.1007/s00039-009-0015-5

Abstract

We study the interplay between the geometry of Hardy spaces and functional analytic properties of singular integral operators (SIO’s), such as the Riesz transforms as well as Cauchy–Clifford and harmonic double-layer operator, on the one hand and, on the other hand, the regularity and geometric properties of domains of locally finite perimeter. Among other things, we give several characterizations of Euclidean balls, their complements, and half-spaces, in terms of the aforementioned SIO’s.

Keywords and phrases

Hardy spaces double-layer potential Riesz transforms Clifford algebras Cauchy–Clifford operator domains of locally finite perimeter SKT domains Clifford–Szegö projections characterizations of balls half-spaces 

2000 Mathematics Subject Classification

Primary: 49Q15 42B20 Secondary 26B15 30G35 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  • Steve Hofmann
    • 1
  • Emilio Marmolejo-Olea
    • 2
  • Marius Mitrea
    • 1
  • Salvador Pérez-Esteva
    • 2
  • Michael Taylor
    • 3
  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA
  2. 2.Instituto de Matemáticas, Unidad CuernavacaUniversidad Nacional Autónoma de MéxicoCuernavacaMéxico
  3. 3.Mathematics DepartmentUniversity of North CarolinaChapel HillUSA

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