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    Dungey, Nick 2005. Riesz transforms on a solvable Lie group of polynomial growth. Mathematische Zeitschrift, Vol. 251, Issue. 3, p. 649.


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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society, Volume 77, Issue 2
  • October 2004, pp. 249-268

Some regularity estimates for convolution semigroups on a group of polynomial growth

  • Nick Dungey (a1)
  • DOI: http://dx.doi.org/10.1017/S1446788700013616
  • Published online: 01 April 2009
Abstract
Abstract

We study a convolution semigroup satisfying Gaussian estimates on a group G of polynomial volume growth. If Q is a subgroup satisfying a certain geometric condition, we obtain high order regularity estimates for the semigroup in the direction of Q. Applications to heat kernels and convolution powers are given.

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[1]G. Alexopoulos , ‘An application of homogenization theory to harmonic analysis: Harnack inequalities and Riesz transforms on Lie groups of polynomial growth’, Canad. J. Math. 44 (1992), 691727.

[6]P. L. Butzer and H. Berens , Semi-groups of operators and approximation, Die Grundlehren der mathematischen Wissenschaften Band 145 (Springer, New York, 1967).

[8]N. Dungey , A. F. M. ter Elst and D. W. Robinson , Analysis on Lie groups with polynomial growth, Progress in Mathematics 214 (Birkhäuser, Boston, MA, 2003).

[9]X. T. Duong and D. W. Robinson , ‘Semigroup kernels, Poisson bounds, and holomorphic functional calculus’, J. Funct. Anal. 142 (1996), 89129.

[11]A. F. M. ter Elst and D. W. Robinson , ‘Weighted subcoercive operators on Lie groups’, J. Funct. Anal. 157 (1998), 88163.

[13]A. F. M. ter Elst , D. W. Robinson and A. Sikora , ‘Riesz transforms and Lie groups of polynomial growth’, J. Funct. Anal. 162 (1999), 1451.

[14]M. Gromov , ‘Groups of polynomial growth and expanding maps’, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 5378.

[15]W. Hebisch and L. Saloff-Coste , ‘Gaussian estimates for Markov chains and random walks on groups’, Ann. Probab. 21 (1993), 673709.

[16]M. S. Raghunathan , Discrete subgroups of Lie groups (Springer, New York, 1972).

[18]L. Saloff-Coste , ‘Analyse sur les groupes de Lie à croissance polynômiale’, Ark. Mat. 28 (1990), 315331.

[19]N. T. Varopoulos , ‘Analysis on nilpotent groups’, J. Funct. Anal. 66 (1986), 406431.

[20]N. T. Varopoulos , ‘Analysis on Lie groups’, J. Funct. Anal. 76 (1988), 346410.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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