Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group
Studia Mathematica, Tome 101 (1991) no. 1, pp. 33-68
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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).
@article{10_4064_sm_101_1_33_68,
author = {Ewa Damek},
title = {Maximal functions related to subelliptic operators invariant under an action of a solvable {Lie} group},
journal = {Studia Mathematica},
pages = {33--68},
publisher = {mathdoc},
volume = {101},
number = {1},
year = {1991},
doi = {10.4064/sm-101-1-33-68},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-101-1-33-68/}
}
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Ewa Damek. Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group. Studia Mathematica, Tome 101 (1991) no. 1, pp. 33-68. doi: 10.4064/sm-101-1-33-68
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