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

• Autorzy: Ewa Damek
• Języki publikacji: EN

Abstrakty

EN

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

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: 1992
• Tom: 103
• Numer: 3
• Strony: 239-264

Daty

wydano

1992

otrzymano

1991-09-11

poprawiono

1992-09-23

Twórcy

autor

Ewa Damek

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

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