Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group

• Autorzy: Ewa Damek , Andrzej Hulanicki
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 58J32: Boundary value problems on manifolds
• 43A85: Analysis on homogeneous spaces
• 22E30: Analysis on real and complex Lie groups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1991-1992
• Tom: 101
• Numer: 1
• Strony: 33-68

Daty

wydano

1991

otrzymano

1990-11-09

poprawiono

1991-07-31

Twórcy

autor

Ewa Damek

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Andrzej Hulanicki

• Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

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