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1992 | 103 | 3 | 239-264
Tytuł artykułu

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

Autorzy
Treść / Zawartość
Warianty tytułu
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
Słowa kluczowe
Czasopismo
Rocznik
Tom
103
Numer
3
Strony
239-264
Opis fizyczny
Daty
wydano
1992
otrzymano
1991-09-11
poprawiono
1992-09-23
Twórcy
autor
  • Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
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  • [DH] E. Damek and A. Hulanicki, Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group, ibid. 101 (1991), 34-68.
  • [FKP] R. A. Fefferman, C. E. Kenig and J. Pipher, The theory of weights and the Dirichlet problem for elliptic equations, Ann. of Math. 134 (1991), 65-124.
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  • [HS] W. Hebisch and A. Sikora, A smooth subadditive homogeneous norm on a homogeneous group, Studia Math. 96 (1990), 231-236.
  • [H1] A. Hulanicki, Subalgebra of $L_1(G)$ associated with Laplacian on a Lie group, Colloq. Math. 31 (1974), 259-287.
  • [H2] A. Hulanicki, A class of convolution semi-groups of measures on a Lie group, in: Lecture Notes in Math. 828, Springer, 1980, 82-101.
  • [HJ] A. Hulanicki and J. Jenkins, Nilpotent groups and summability of eigenfunction expansions of Schrödinger operators, Studia Math. 80 (1984), 235-244.
  • [Ko] J. J. Kohn, Pseudo-differential operators and non-elliptic problems, in: Pseudo-differential Operators, CIME Conference, Stresa 1968, Ed. Cremonese, Roma 1969, 157-165.
  • [St] E. M. Stein, Boundary behavior of harmonic functions on symmetric spaces: maximal estimates for Poisson integrals, Invent. Math. 74 (1983), 63-83.
  • [SW] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971.
  • [S] D. Stroock, Lectures on Stochastic Analysis: Diffusion Theory, Cambridge Univ. Press, 1987.
  • [SV] D. Stroock and S. R. Varadhan, Multidimensional Diffusion Processes, Springer, 1979.
  • [T] J. C. Taylor, Skew products, regular conditional probabilities and stochastic differential equations: a remark, preprint.
  • [Z] J. Zienkiewicz, A maximal operator related to a nonsymmetric semigroup generated by a left-invariant operator on a Lie group, submitted to Studia Math.
Typ dokumentu
Bibliografia
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