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

Tom 101 / 1991

Ewa Damek Studia Mathematica 101 (1991), 33-68 DOI: 10.4064/sm-101-1-33-68

Streszczenie

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).

Autorzy

  • Ewa Damek

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