On the Hardy space-H of a \(C^ 1\) domain

DOI10.1007/BF02384466zbMath0484.42006MaRDI QIDQ1163708

Eugene B. Fabes, Carlos E. Kenig

Publication date: 1981

Published in: Arkiv för Matematik (Search for Journal in Brave)

zbMATH Keywords

harmonic functionatomBMOPoisson integralCarleson measureRiesz transform

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Banach algebras of differentiable or analytic functions, (H^p)-spaces (46J15) (H^p)-spaces (42B30) Banach spaces of continuous, differentiable or analytic functions (46E15)

Related Items (12)

Adjoint boundary value problems for the biharmonic equation on \(C^ 1\) domains in the plane ⋮ Stress potentials on \(C^ 1\) domains ⋮ Vector potential theory on nonsmooth domains in \(\mathbb{R}^ 3\) and applications to electromagnetic scattering ⋮ Dirichlet problem for the heat equation in \(h_ c^ 1(d\omega)\) ⋮ Traces of functions in Hardy and Besov spaces on Lipschitz domains with applications to compensated compactness and the theory of Hardy and Bergman type spaces ⋮ Hardy Spaces for the Three-Dimensional Vekua Equation ⋮ Nonsymmetric systems on nonsmooth planar domains ⋮ Generalized Dirac operators on nonsmooth manifolds and Maxwell's equations ⋮ Elliptic Partial Differential Equations with Almost-Real Coefficients ⋮ Local Riesz transform and local Hardy spaces on Riemannian manifolds with bounded geometry ⋮ Decomposition of $L^{2}$-Vector Fields on Lipschitz Surfaces: Characterization via Null-Spaces of the Scalar Potential ⋮ Boundary behavior of harmonic functions in non-tangentially accessible domains

Cites Work

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• On the theory of harmonic functions of several variables
• BMO functions and the \(\overline\partial\)-equation
• Potential techniques for boundary value problems on \(C^1\)-domains
• Estimates of harmonic measure
• \(H^p\) spaces of several variables
• On the Poisson integral for Lipschitz and $C^{1}$-domains
• Weighted norm inequalities for the Lusin area integral and the nontangential maximal functions for functions harmonic in a Lipschitz domain
• Extensions of Hardy spaces and their use in analysis
• Cauchy integrals on Lipschitz curves and related operators
• On Functions Subharmonic in a Lipschitz Domain
• A characterization of $H^{p}(R^{n})$ in terms of atoms
• A real variable characterization of $H^{p}$
• On the Boundary Values of Harmonic Functions
• Characterizations of bounded mean oscillation

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