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

Ewa Damek

Studia Mathematica (1992)

  • Volume: 103, Issue: 3, page 239-264
  • ISSN: 0039-3223

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Damek, Ewa. "Maximal functions related to subelliptic operators invariant under an action of a nilpotent Lie group." Studia Mathematica 103.3 (1992): 239-264. <http://eudml.org/doc/215948>.

@article{Damek1992,
abstract = {},
author = {Damek, Ewa},
journal = {Studia Mathematica},
keywords = {simply connected nilpotent Lie group; subelliptic operators; -harmonic function; Poisson integral; maximal functions; weak type ; harmonic measures},
language = {eng},
number = {3},
pages = {239-264},
title = {Maximal functions related to subelliptic operators invariant under an action of a nilpotent Lie group},
url = {http://eudml.org/doc/215948},
volume = {103},
year = {1992},
}

TY - JOUR
AU - Damek, Ewa
TI - Maximal functions related to subelliptic operators invariant under an action of a nilpotent Lie group
JO - Studia Mathematica
PY - 1992
VL - 103
IS - 3
SP - 239
EP - 264
AB -
LA - eng
KW - simply connected nilpotent Lie group; subelliptic operators; -harmonic function; Poisson integral; maximal functions; weak type ; harmonic measures
UR - http://eudml.org/doc/215948
ER -

References

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  2. [D] E. Damek, Left-invariant degenerate elliptic operators on semidirect extensions of homogeneous groups, Studia Math. 89 (1988), 169-196. Zbl0675.22005
  3. [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. Zbl0811.43001
  4. [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. Zbl0770.35014
  5. [FS] G. B. Folland and E. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, 1982. Zbl0508.42025
  6. [GT] D. Gilbarg and N. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 1983. Zbl0562.35001
  7. [HS] W. Hebisch and A. Sikora, A smooth subadditive homogeneous norm on a homogeneous group, Studia Math. 96 (1990), 231-236. Zbl0723.22007
  8. [H1] A. Hulanicki, Subalgebra of L 1 ( G ) associated with Laplacian on a Lie group, Colloq. Math. 31 (1974), 259-287. Zbl0316.43005
  9. [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. 
  10. [HJ] A. Hulanicki and J. Jenkins, Nilpotent groups and summability of eigenfunction expansions of Schrödinger operators, Studia Math. 80 (1984), 235-244. Zbl0564.43007
  11. [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. 
  12. [St] E. M. Stein, Boundary behavior of harmonic functions on symmetric spaces: maximal estimates for Poisson integrals, Invent. Math. 74 (1983), 63-83. 
  13. [SW] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971. 
  14. [S] D. Stroock, Lectures on Stochastic Analysis: Diffusion Theory, Cambridge Univ. Press, 1987. Zbl0605.60057
  15. [SV] D. Stroock and S. R. Varadhan, Multidimensional Diffusion Processes, Springer, 1979. Zbl0426.60069
  16. [T] J. C. Taylor, Skew products, regular conditional probabilities and stochastic differential equations: a remark, preprint. Zbl0763.60031
  17. [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. 

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