Poisson integrals and semisimple groups

DOI10.1007/BF02790369zbMath0247.31002MaRDI QIDQ2555945

R. E. Williamson, A. W. Knapp

Publication date: 1971

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (11)

Eigenfunctions of the Laplace-Beltrami operator on harmonic \(NA\) groups ⋮ The cohomology of semi-simple Lie groups, viewed from infinity ⋮ Fatou Theorems for Eigenfunctions of the Invariant Differential Operators on Symmetric Spaces ⋮ On the Boundary Behaviour of Generalized Poisson Integrals on Symmetric Spaces ⋮ Characterization of almost 𝐿^{𝑝}-eigenfunctions of the Laplace-Beltrami operator ⋮ Characterization of the Lp-range of the Poisson transform on the Octonionic Hyperbolic Plane ⋮ Representations of complex semisimple Lie groups ⋮ Invariant measures of horospherical flows on non-compact homogeneous spaces ⋮ Fatou's theorem for symmetric spaces ⋮ Boundary behavior of harmonic functions on symmetric spaces: maximal estimates for Poisson integrals ⋮ A Fatou theorem for eigenfunctions of the Laplace-Beltrami operator in a symmetric space

Cites Work

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• Fatou's theorem for symmetric spaces. I
• Pointwise limits for sequences of convolution operators
• A Poisson formula for semi-simple Lie groups
• Harmonic and Analytic Functions Of Several Variables and The Maximal Theorem Of Hardy and Littlewood
• Spherical Functions on a Semisimple Lie Group, I
• A Fatou-type theorem for harmonic functions on symmetric spaces
• Compactifications of Symmetric Spaces
• Boundary Behavior of Poisson Integrals on Symmetric Spaces
• Note on the differentiability of multiple integrals

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