Displaying similar documents to “Maximal functions related to subelliptic operators invariant under an action of a nilpotent Lie group”

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

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).

Hardy space estimates for multilinear operators (II).

Loukas Grafakos (1992)

Revista Matemática Iberoamericana

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We continue the study of multilinear operators given by products of finite vectors of Calderón-Zygmund operators. We determine the set of all r ≤ 1 for which these operators map products of Lebesgue spaces L(R) into the Hardy spaces H(R). At the endpoint case r = n/(n + m + 1), where m is the highest vanishing moment of the multilinear operator, we prove a weak type result.