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Derivatives of kernels associated to complex subelliptic operators

Published online by Cambridge University Press:  17 April 2009

A. F. M. ter Elst
A. F. M. ter Elst
Affiliation:
Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia
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Abstract

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We prove large time Gaussian bounds for the derivatives of the semigroups kernel associated with complex, second-order, subelliptic operators on Lie groups of polynomial growth.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 67 , Issue 3 , June 2003 , pp. 393 - 406
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Alexopoulos, G., ‘An application of homogenization theory of harmonic analysis: Harnack inequalities and Riesz transforms on Lie groups of polynomial growth’, Canad. J. Math. 44 (1992), 691–727.CrossRefGoogle Scholar
[2]Alexopoulos, G., ‘An application of homogenization theory to harmonic analysis on solvable Lie groups of polynomial growth’, Pacific J. Math. 159 (1993), 19–45.CrossRefGoogle Scholar
[3]Dungey, N., ‘High order regularity for subelliptic operators on Lie groups of polynomial growth’, (Research Report MRR02–006, The Australian National University, Canberra, Australia, 2002).Google Scholar
[4]Dungey, N., Private communication.Google Scholar
[5]ter Elst, A.F.M. and Robinson, D.W., ‘Subcoercive and subelliptic operators on Lie groups: variable coefficients’, Publ. Res. Inst. Math. Sci. 29 (1993), 745–801.CrossRefGoogle Scholar
[6]ter Elst, A.F.M. and Robinson, D.W., ‘Subelliptic operators on Lie groups: regularity’, J. Austr. Math. Soc. Ser. A 57 (1994), 179–229.CrossRefGoogle Scholar
[7]ter Elst, A.F.M. and Robinson, D.W., ‘Weighted subcoercive operators on Lie groups’, J. Funct. Anal. 157 (1998), 88–163.CrossRefGoogle Scholar
[8]ter Elst, A.F.M. and Robinson, D.W., ‘Second-order subelliptic operators on Lie groups III: Hölder continuous coefficients’, Calc. Var. Partial Differential Equations 8 (1999), 327–363.CrossRefGoogle Scholar
[9]ter Elst, A.F.M. and Robinson, D.W., ‘Gaussian bounds for complex subelliptic operators on Lie groups of polynomial growth’, Bull. Austral. Math. Soc. 67 (2003), 201–218.CrossRefGoogle Scholar
[10]ter Elst, A.F.M., Robinson, D.W. and Sikora, A., ‘Heat kernels and Riesz transforms on nilpotent Lie groups’, Coll. Math. 74 (1997), 191–218.CrossRefGoogle Scholar
[11]ter Elst, A.F.M., Robinson, D.W. and Sikora, A., ‘Riesz transforms and Lie groups of polynomial growht’, J. Funct. Anal. 162 (1999), 14–51.CrossRefGoogle Scholar
[12]Robinson, D.W., Elliptic operators and Lie groups, Oxford Mathematical Monographs (Oxford University Press, New York, 1991).CrossRefGoogle Scholar
[13]Saloff-Coste, L., ‘Analyse sur les groupes de Lie à croissance polynȏmiale’, Ark. Mat. 28 (1990), 315–331.CrossRefGoogle Scholar
[14]Varadarajan, V.S., Lie groups, Lie algebras, and their representations, Graduate Texts in Mathematics 102 (Springer-Verlag, New York, 1984).CrossRefGoogle Scholar
[15]Varopoulos, N.T., Saloff-Coste, L. and Coulhon, T., Analysis and geometry on groups, Cambridge Tracts in Mathematics 100 (Cambridge University Press, Cambridge, 1992).Google Scholar