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

Part of: Partial differential equations Lie groups

Published online by Cambridge University Press:  09 April 2009

Nick Dungey
Nick Dungey
Affiliation:
School of Mathematics, University fo New South Wales, Sydney 2052, Australia e-mail: [email protected]
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Abstract

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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.

MSC classification

Secondary: 22E30: Analysis on real and complex Lie groups 35B40: Asymptotic behavior of solutions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 77 , Issue 2 , October 2004 , pp. 249 - 268
Copyright
Copyright © Australian Mathematical Society 2004

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