A Generalized Fatou Theorem

DOI10.2307/2000365zbMath0657.31011OpenAlexW4253386079MaRDI QIDQ3805022

David Singman, Bernard A. Mair

Publication date: 1987

Full work available at URL: https://doi.org/10.2307/2000365

zbMATH Keywords

heat equationmaximal functionFatou theoremparabolic equationsLaplace's equationpseudo-distance\(\alpha\)-admissibleboundary limitsweak typedegree of tangency\(\Omega\)-Lebesgue setintegrals of kernels

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Initial-boundary value problems for second-order parabolic equations (35K20) Heat equation (35K05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary behavior of harmonic functions in higher dimensions (31B25)

Related Items (6)

Weighted weak-type inequalities for the maximal function of nonnegative integral transforms over approach regions ⋮ Boundary behaviour of harmonic functions and solutions of parabolic systems ⋮ Boundary behavior of superharmonic functions satisfying nonlinear inequalities in uniform domains ⋮ The Besicovitch covering lemma and maximal functions ⋮ Generalized Local Fatou Theorems and Area Integrals ⋮ Foundations of Fatou theory and a tribute to the work of E. M. Stein on boundary behavior of holomorphic functions

Cites Work

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• On certain maximal functions and approach regions
• Integral representations for positive solutions of the heat equation on some unbounded domains
• Analyse harmonique non-commutative sur certains espaces homogènes. Etude de certaines intégrales singulières. (Non-commutative harmonic analysis on certain homogeneous spaces. Study of certain singular integrals.)
• Relative limit theorems in analysis
• Boundary Behavior of Positive Solutions of the Heat Equation on a Semi-Infinite Slab
• Non-tangential limits of a solution of a boundary-value problem for the heat equation
• Representation Theorems and Fatou Theorems for Second-Order Linear Parabolic Partial Differential Equations
• Temperatures in Several Variables: Kernel Functions, Representations, and Parabolic Boundary Values

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