Smoothness of densities of semigroups of measures on homogeneous groups

Jacek Dziubański; Jacek Zienkiewicz

Colloquium Mathematicae (1993)

  • Volume: 66, Issue: 2, page 227-242
  • ISSN: 0010-1354

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Dziubański, Jacek, and Zienkiewicz, Jacek. "Smoothness of densities of semigroups of measures on homogeneous groups." Colloquium Mathematicae 66.2 (1993): 227-242. <http://eudml.org/doc/210245>.

@article{Dziubański1993,
author = {Dziubański, Jacek, Zienkiewicz, Jacek},
journal = {Colloquium Mathematicae},
keywords = {positive symmetric measures; homogeneous group; Lévy measure; Lie algebra; nonnegative symmetric function; holomorphic semigroups; Hilbert spaces; differential operator; Malliavin calculus; jump processes},
language = {eng},
number = {2},
pages = {227-242},
title = {Smoothness of densities of semigroups of measures on homogeneous groups},
url = {http://eudml.org/doc/210245},
volume = {66},
year = {1993},
}

TY - JOUR
AU - Dziubański, Jacek
AU - Zienkiewicz, Jacek
TI - Smoothness of densities of semigroups of measures on homogeneous groups
JO - Colloquium Mathematicae
PY - 1993
VL - 66
IS - 2
SP - 227
EP - 242
LA - eng
KW - positive symmetric measures; homogeneous group; Lévy measure; Lie algebra; nonnegative symmetric function; holomorphic semigroups; Hilbert spaces; differential operator; Malliavin calculus; jump processes
UR - http://eudml.org/doc/210245
ER -

References

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  1. [BG] T. Byczkowski and P. Graczyk, Malliavin calculus for stable processes on Heisenberg group, Probab. Math. Statist. 13 (1992), 277-292. Zbl0785.60028
  2. [Da] E. B. Davies, One Parameter Semigroups, Academic Press, 1980. Zbl0457.47030
  3. [Du] M. Duflo, Représentations de semi-groupes de mesures sur un groupe localement compact, Ann. Inst. Fourier (Grenoble) 28 (3) (1978), 225-249. Zbl0368.22006
  4. [Dz] J. Dziubański, On semigroups generated by subelliptic operators on homogeneous groups, Colloq. Math. 64 (1993), 215-231. Zbl0837.43010
  5. [FS] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton University Press, 1982. Zbl0508.42025
  6. [G] P. Głowacki, Stable semi-groups of measures as commutative approximate identities on non-graded homogeneous groups, Invent. Math. 83 (1986), 557-582. Zbl0595.43006
  7. [G1] P. Głowacki, Lipschitz continuity of densities of stable semigroups of measures, Colloq. Math. 66 (1993), 29-47. Zbl0837.43009
  8. [GH] P. Głowacki and A. Hulanicki, A semi-group of probability measures with non-smooth differentiable densities on a Lie group, ibid. 51 (1987), 131-139. Zbl0629.43001
  9. [HS] W. Hebisch and A. Sikora, A smooth subadditive homogeneous norm on a homogeneous group, Studia Math. 96 (1990), 231-236. Zbl0723.22007
  10. [HN] B. Helffer et J. Nourrigat, Caractérisation des opérateurs hypoelliptiques homogènes invariants à gauche sur un groupe nilpotent gradué, Comm. Partial Differential Equations 4 (1979), 899-958. Zbl0423.35040
  11. [H] A. Hulanicki, A class of convolution semi-groups of measures on a Lie group, in: Lecture Notes in Math. 828, Springer, 1980, 82-101. Zbl0462.28009
  12. [Hu] G. A. Hunt, Semi-groups of measures on Lie groups, Trans. Amer. Math. Soc. 81 (1956), 264-293. Zbl0073.12402
  13. [S] E. M. Stein, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory, Princeton Univ. Press, 1970. Zbl0193.10502

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