Hardy spaces, singular integrals and the geometry of Euclidean domains of locally finite perimeter

DOI10.1007/s00039-009-0015-5zbMath1333.42020OpenAlexW1996797096MaRDI QIDQ1047122

Marius Mitrea, Salvador Pérez-Esteva, Michael E. Taylor, Emilio Marmolejo Olea, Steven Hofmann

Publication date: 4 January 2010

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00039-009-0015-5

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Functions of hypercomplex variables and generalized variables (30G35) Length, area, volume, other geometric measure theory (28A75)

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Cites Work

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• Chord-arc surfaces with small constant. I
• Boundary behavior of harmonic functions in non-tangentially accessible domains
• The Cauchy kernel, the Szegö kernel, and the Riemann mapping function
• Courbes corde-arc et espaces de Hardy généralisés
• L'intégrale de Cauchy définit un opératuer borne sur \(L^ 2 \)pour les courbes lipschitziennes
• Radial symmetry for elliptic boundary-value problems on exterior domains
• Szegö and Bergman projections on non-smooth planar domains
• Geometric measure theory.
• Radial symmetry for an electrostatic, a capillarity and some fully nonlinear overdetermined problems on exterior domains
• Free boundary regularity for harmonic measures and Poisson kernels
• Geometric and transformational properties of Lipschitz domains, Semmes-Kenig-Toro domains, and other classes of finite perimeter domains
• The kerzman-stein theorem on the sphere
• On a free boundary problem in electrostatics
• Some methods for studying stability in isoperimetric type problems
• Weakly Differentiable Functions
• On Some Maximum Principles Involving Harmonic Functions and Their Derivatives
• Poisson kernel characterization of Reifenberg flat chord arc domains
• Electrostatic characterization of spheres
• Symmetry of a boundary integral operator and a characterization of a ball