Pointwise estimates for the Poisson kernel on NA groups by the Ancona method
Ewa Damek (1996)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Ewa Damek (1996)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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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, Andrzej Hulanicki, Jacek Zienkiewicz (1997)
Studia Mathematica
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For rank one solvable Lie groups of the type NA estimates for the Poisson kernels and their derivatives are obtained. The results give estimates on the Poisson kernel and its derivatives in a natural parametrization of the Poisson boundary (minus one point) of a general homogeneous, simply connected manifold of negative curvature.
Ewa Damek (1992)
Studia Mathematica
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Ronald Coifman, Guido Weiss (1972)
Studia Mathematica
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Ewa Damek (1997)
Colloquium Mathematicae
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G. Folland (1979)
Studia Mathematica
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Ewa Damek, Andrzej Hulanicki (2000)
Studia Mathematica
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Let D be a symmetric irreducible Siegel domain. Pluriharmonic functions satisfying a certain rather weak growth condition are characterized by r+2 operators (r+1 in the tube case), r being the rank of the underlying symmetric cone
Francesca Astengo, Bianca di Blasio (1999)
Colloquium Mathematicae
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Let N be an H-type group and consider its one-dimensional solvable extension NA, equipped with a suitable left-invariant Riemannian metric. We prove a Paley-Wiener theorem for nonradial functions on NA supported in a set whose boundary is a horocycle of the form Na, a ∈ A.
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.