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1994 | 67 | 2 | 197-216
Tytuł artykułu

On positive Rockland operators

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G be a homogeneous Lie group with a left Haar measure dg and L the action of G as left translations on $L_p(G;dg)$. Further, let H = dL(C) denote a homogeneous operator associated with L. If H is positive and hypoelliptic on $L_2$ we prove that it is closed on each of the $L_p$-spaces, p ∈ 〈 1,∞〉, and that it generates a semigroup S with a smooth kernel K which, with its derivatives, satisfies Gaussian bounds. The semigroup is holomorphic in the open right half-plane on all the $L_p$-spaces, p ∈ [1,∞]. Further extensions of these results to nonhomogeneous operators and general representations are also given.
Słowa kluczowe
Rocznik
Tom
67
Numer
2
Strony
197-216
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-09-14
Twórcy
  • IRMAR, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France
  • Department of Mathematics, and Computing Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
  • Centre for Mathematics and its Applications School of Mathematical Sciences Australian National University Canberra, ACT 0200 Australia
Bibliografia
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  • [BrR2] O. Bratteli and D. W. Robinson, Subelliptic operators on Lie groups: variable coefficients, Acta Appl. Math. (1994), to appear.
  • [BER] R. J. Burns, A. F. M. ter Elst and D. W. Robinson, $L_p$-regularity of subelliptic operators on Lie groups, J. Operator Theory 30 (1993), to appear.
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  • [DHZ] J. Dziubański, W. Hebisch and J. Zienkiewicz, Note on semigroups generated by positive Rockland operators on graded homogeneous groups, Studia Math. 110 (1994), 115-126.
  • [ElR1] A. F. M. ter Elst and D. W. Robinson, Subcoercivity and subelliptic operators on Lie groups II: The general case, Potential Anal. (1994), to appear.
  • [ElR2] A. F. M. ter Elst and D. W. Robinson, Subcoercive and subelliptic operators on Lie groups: variable coefficients, Publ. RIMS Kyoto Univ. 29 (1993), 745-801.
  • [ElR3] A. F. M. ter Elst and D. W. Robinson, Functional analysis of subelliptic operators on Lie groups, J. Operator Theory 30 (1993), to appear.
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  • [HeN2] B. Helffer et J. Nourrigat, Hypoellipticité maximale pour des opérateurs polynômes de champs de vecteurs, Progr. Math. 58, Birkhäuser, Boston, 1985.
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  • [NeS] E. Nelson and W. F. Stinespring, Representation of elliptic operators in an enveloping algebra, Amer. J. Math. 81 (1959), 547-560.
  • [Nir] L. Nirenberg, Remarks on strongly elliptic partial differential operators, Comm. Pure Appl. Math. 8 (1955), 649-675.
  • [Rob] D. W. Robinson, Elliptic Operators and Lie Groups, Oxford Math. Monographs, Oxford University Press, Oxford, 1991.
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  • [VSC] N. T. Varopoulos, L. Saloff-Coste and T. Coulhon, Analysis and Geometry on Groups, Cambridge Tracts in Math. 100, Cambridge University Press, Cambridge, 1992.
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Bibliografia
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bwmeta1.element.bwnjournal-article-cmv67i2p197bwm
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