J. Aust. Math. Soc.  77 (2004), 249-268
Some regularity estimates for convolution semigroups on a group of polynomial growth

Nick Dungey
  School of Mathematics
  University fo New South Wales
  Sydney 2052

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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