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1994 | 110 | 2 | 115-126
Tytuł artykułu

Note on semigroups generated by positive Rockland operators on graded homogeneous groups

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let L be a positive Rockland operator of homogeneous degree d on a graded homogeneous group G and let $p_t$ be the convolution kernels of the semigroup generated by L. We prove that if τ(x) is a Riemannian distance of x from the unit element, then there are constants c>0 and C such that $|p_1(x)| ≤ Cexp(-cτ(x)^{d/(d-1)})$. Moreover, if G is not stratified, more precise estimates of $p_1$ at infinity are given.
Słowa kluczowe
Czasopismo
Rocznik
Tom
110
Numer
2
Strony
115-126
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-03-29
poprawiono
1993-10-25
Twórcy
  • Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
  • Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
  • [D] J. Dziubański, On semigroups generated by subelliptic operators on homogeneous groups, Colloq. Math. 64 (1993), 215-231.
  • [DH] J. Dziubański and A. Hulanicki, On semigroups generated by left-invariant positive differential operators on nilpotent Lie groups, Studia Math. 94 (1989), 81-95.
  • [FS] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Princeton Univ. Press, Princeton, 1982.
  • [He] W. Hebisch, Sharp pointwise estimates for the kernels of the semigroup generated by sums of even powers of vector fields on homogeneous groups, Studia Math. 95 (1989), 93-106.
  • [He1] W. Hebisch, Estimates on the semigroups generated by left invariant operators on Lie groups, J. Reine Angew. Math. 423 (1992), 1-45.
  • [HS] W. Hebisch and A. Sikora, A smooth subadditive homogeneous norm on a homogeneous group, Studia Math. 96 (1990), 231-236.
  • [HN] B. Helffer et J. Nourrigat, Caractérisation des opérateurs hypoelliptiques homogènes à gauche sur un groupe nilpotent gradué, Comm. Partial Differential Equations 4 (1979), 899-958.
  • [H] A. Hulanicki, Subalgebra of $L^1(G)$ associated with laplacian on a Lie group, Colloq. Math. 31 (1974), 259-287.
  • [HJ] A. Hulanicki and J. W. Jenkins, Nilpotent Lie groups and summability of eigenfunction expansions of Schrödinger operators, Studia Math. 80 (1984), 235-244.
  • [J] J. W. Jenkins, Dilations and gauges on nilpotent Lie groups, Colloq. Math. 41 (1979), 91-101.
  • [NRS] A. Nagel, F. Ricci and E. M. Stein, Harmonic analysis and fundamental solutions on nilpotent Lie groups, in: Analysis and Partial Differential Equations, Marcel Dekker, 1990, 249-275.
  • [P] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv110i2p115bwm
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