Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups
Ewa Damek (1988)
Studia Mathematica
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Ewa Damek (1988)
Studia Mathematica
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Ewa Damek, Andrzej Hulanicki (1991)
Studia Mathematica
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On the domain S_a = {(x,e^b): x ∈ N, b ∈ ℝ, b > a} where N is a simply connected nilpotent Lie group, a certain N-left-invariant, second order, degenerate elliptic operator L is considered. N × {e^a} is the Poisson boundary for L-harmonic functions F, i.e. F is the Poisson integral F(xe^b) = ʃ_N f(xy)dμ^b_a(x), for an f in L^∞(N). The main theorem of the paper asserts that the maximal function M^a f(x) = sup{|ʃf(xy)dμ_a^b(y)| : b > a} is of weak type (1,1).
Ewa Damek (1996)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Ewa Damek, Andrzej Hulanicki, Roman Urban (2001)
Revista Matemática Iberoamericana
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In this paper we treat noncoercive operators on simply connected manifolds of negative curvature.
Joseph G. Conlon, Peder A. Olsen (1997)
Revista Matemática Iberoamericana
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In this paper we continue the study of the Dirichlet problem for an elliptic equation on a domain in R3 which was begun in [5]. For R > 0 let ΩR be the ball of radius R centered at the origin with boundary ∂Ω R. The Dirichlet problem we are concerned with is the following: (-Δ - b(x).∇) u(x) = f(x), x ∈ Ω R, with zero boundary conditions ...
G. Folland (1979)
Studia Mathematica
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Olof Svensson (1996)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Yasushi Ishikawa (1997)
Annales de l'I.H.P. Probabilités et statistiques
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