Maximal functions related to subelliptic operators invariant under an action of a nilpotent Lie group
Studia Mathematica, Tome 103 (1992) no. 3, pp. 239-264
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On the domain $Ω_a = {(x,b) : x ∈ N, b ∈ ℝ^+, b > a}$, where N is a simply connected nilpotent Lie group and a ≥ 0, certain N-invariant second order subelliptic operators L are considered. Every bounded L-harmonic function F is the Poisson integral $F(x,b) = f ∗ μ̌_a^b(x)$ for an $f ∈ L^∞(N)$. The main theorem of the paper asserts that under some assumptions the maximal functions $M_1f(x) = sup_{b≥a+1} |f∗μ̌_a^b(x)|$, $M_2f(x) = sup_{a
@article{10_4064_sm_103_3_239_264,
author = {Ewa Damek},
title = {Maximal functions related to subelliptic operators invariant under an action of a nilpotent {Lie} group},
journal = {Studia Mathematica},
pages = {239--264},
publisher = {mathdoc},
volume = {103},
number = {3},
year = {1992},
doi = {10.4064/sm-103-3-239-264},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-103-3-239-264/}
}
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Ewa Damek. Maximal functions related to subelliptic operators invariant under an action of a nilpotent Lie group. Studia Mathematica, Tome 103 (1992) no. 3, pp. 239-264. doi: 10.4064/sm-103-3-239-264
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