A Fatou theorem for eigenfunctions of the Laplace-Beltrami operator in a symmetric space

DOI10.1215/S0012-7094-84-05103-2zbMath0543.43007OpenAlexW1506913513MaRDI QIDQ796030

Peter Sjögren

Publication date: 1984

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-84-05103-2

zbMATH Keywords

Martin boundaryLaplace-Beltrami operatorFatou theoremPoisson kernelmaximal functionsjoint eigenfunctionRiemannian symmetric spaceFürstenberg boundary

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Harmonic analysis on homogeneous spaces (43A85) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10)

Related Items (3)

Fractional Laplacians and extension problems: The higher rank case ⋮ Fatou theorem and its converse for positive eigenfunctions of the Laplace-Beltrami operator on harmonic \textit{NA} groups ⋮ On the Boundary Behaviour of Generalized Poisson Integrals on Symmetric Spaces

Cites Work

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• Boundary behavior of harmonic functions on symmetric spaces: maximal estimates for Poisson integrals
• Poisson integrals and semisimple groups
• Spherical Functions on a Semisimple Lie Group, I
• Maximal functions: Poisson integrals on symmetric spaces
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Fatou theorems and maximal functions for eigenfunctions of the Laplace-Beltrami operator in a bidisk.
• Fatou Theorems for Eigenfunctions of the Invariant Differential Operators on Symmetric Spaces

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